1. A company is planning to manufacture snowboards. The fixed costs are $400 per day and...
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1. A company is planning to manufacture snowboards. The fixed costs are $400 per day and total costs are $6200 per day at a daily output of 20 boards. A. Assuming that the total cost per day, C(x), is linearly related to the total output per day, x, write an equation for the cost function. C(x) = B. The average cost per board for an output of x boards is given by C(x)=C(x)/x. Find the average cost function. C(x)= C. Sketch a graph of the average cost function, including any asymptotes, for 1 ≤x≤30. Choose the correct graph below. 500- ELL D. What does the average cost per board tend to as production increases? 500- 30 500- 30 OD. 500 30 ci Most appliance manufacturers produce conventional and energy-efficient models. The energy-efficient models are more expensive to make but cheaper to operate. The costs of purchasing and operating a 25-cubic-foot appliance of each type are given in the table. These costs do not include maintenance charges or changes in electricity prices. Energy-Efficient Model Initial cost Total volume Annual cost of electricity $550 25 ft³ $60 Conventional Model a) Express the total cost C₂(x) and the average cost C₂(x)-Ce(x)/x of purchasing and operating an energy-efficient model for x years. C₂(x) = T.(x) = b) Express the total cost C₂(x) and the average cost C₂(x)=C₂(x)/x of purchasing and operating a conventional model for x years. OA The total costs are the same after OB. The total costs will never be the same. C₂(x)- C.(x)- c) Are the total costs for an energy-efficient model and for a conventional model ever the same? If so, when? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. years. $490 25 ft³ $80 d) Are the average costs for an energy-efficient model and for a conventional model ever the same? If so, when? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. QA. The average costs are the same after years. OB. The average costs will never be the same. e) Find the limit of Ce(x) as x→∞. Dann 2. (cont.) lim C₂(x) = Find the limit of C, (x) as x→∞. lim C₂(x) = Choose the correct implications of the results. OA Over time the average cost of purchasing and operating an energy-efficient model will be more expensive than a conventional model. OB. Over time the average cost of purchasing and operating an energy-efficient model will have the same cost as a conventional model. OC. Over time the average cost of purchasing and operating an energy-efficient model will be cheaper than a conventional model. 3. The revenue (in dollars) from the sale of x car seats for infants is given by the following function. R(x)=24x-0.010x² 0≤x≤2400 (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (B) Use the four-step process to find R'(x). (C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car scats. (Round to one decimal place as needed.) (B) R'(x)= (C) R(1000)- R'(1000) = Interpret these results. Choose the correct answer below. CA. This means that at a production level of 1,000 car seats, the revenue is R'(1000) dollars and is increasing at a rate of R(1000) dollars per seat. OB. This means that at a production level of 1,000 car seats, the revenue is R(1000) dollars and is decreasing at a rate of R'(1000) dollars per seat. OC. This means that at a production level of 1,000 car seats, the revenue is R(1000) dollars and is increasing at a rate of R'(1000) dollars per seat. 4. The total sales of a company (in millions of dollars) t months from now are given by the following formula. S(t) = 9Vt+10 (A) Use the four-step process to find S'(t). (B) Find S(15) and S'(15). (C) Use the results in part (B) to estimate the total sales after 16 months and 17 months. (A) S'(t)- (B) S(15)-(Type an integer or a decimal.) S'(15)= (Type an integer or a decimal.) (C) S(16) (Type an integer or a decimal.) S(17) RS B (Type an integer or a decimal.) 5. The total sales of a company (in millions of dollars) t months from now are given by S(t)-0.031³ +0.41²+71+5. (A) Find S'(t). (B) Find S(7) and S'(7) (to two decimal places). (C) Interpret S(12)=198.44 and S'(12) = 29.56. (A) S'(1) - (B) S(7)= $'(7) - (C) Choose the correct interpretation of S(12)=198.44. CA The total sales 12 months from now will be $198.44 million dollars. OB. In 12 months the sales will be increasing at a rate of $198.44 million per month. Cc. In approximately 198 months the sales will be increasing by $12 million per month. CD. In approximately 198 months the sales will be $12 million dollars. Choose the correct interpretation of S'(12) = 29.56. OA In approximately 30 months the sales will be increasing by $12 million per month. OB. In 12 months the sales will be increasing at a rate of $29.56 million per month. OC. In approximately 30 months the sales will be $12 million dollars. OD. The total sales 12 months from now will be $29.56 million dollars. 6. The total sales of a company (in millions of dollars) t months from now are given by S(t)=0.02t¹ +0.3t²+8t+3. (A) Find S'(t). (B) Find S(3) and S'(3) (to two decimal places). (C) Interpret S(8)=96.44 and S'(8) - 16.64. (A) S'(0) = (B) S(3)- S'(3)= (C) Choose the correct interpretation of S(8)= 96.44. QA The total sales 8 months from now will be $96.44 million dollars. OB. In approximately 96 months the sales will be $8 million dollars. OC. In approximately 96 months the sales will be increasing by $8 million per month. OD. In 8 months the sales will be increasing at a rate of $96.44 million per month. Choose the correct interpretation of S'(8) = 16.64. OA. In 8 months the sales will be increasing at a rate of $16.64 million per month. OB. In approximately 17 months the sales will be $8 million dollars. Oo. The total sales 8 months from now will be $16.64 million dollars. OD. In approximately 17 months the sales will be increasing by $8 million per month. 7. The total sales of a company (in millions of dollars) t months from now are given by S(t)=0.04t² +0.4t² +7t+2. (A) Find S'(t). (B) Find S(5) and S'(5) (to two decimal places). (C) Interpret S(8)=104.08 and S'(8) = 21.08. (A) S'(t) = (B) S(5)- S'(5) - (C) Choose the correct interpretation of S(8) - 104.08. QA In approximately 104 months the sales will be $8 million dollars. OB. The total sales 8 months from now will be $104.08 million dollars. Oc. In approximately 104 months the sales will be increasing by $8 million per month. OD. In 8 months the sales will be increasing at a rate of $104.08 million per month. Choose the correct interpretation of S'(8)-21.08. OA The total sales 8 months from now will be $21.08 million dollars. OB. In approximately 21 months the sales will be $8 million dollars. Oc. In approximately 21 months the sales will be increasing by $8 million per month. QD. In 8 months the sales will be increasing at a rate of $21.08 million per month. po The total sales of a company (in millions of dollars) 1 months from now are given by S(t)=0.04t² +0.2t² +8t+2. (A) Find S'(t). (B) Find S(5) and S'(5) (to two decimal places). (C) Interpret S(8)=99.28 and S'(8) -18.88. (A) S'(1) - (B) S(5)= S'(5)= (C) Choose the correct interpretation of S(8)= 99.28. OA The total sales 8 months from now will be $99.28 million dollars. OB. In 8 months the sales will be increasing at a rate of $99.28 million per month. Oc. In approximately 99 months the sales will be increasing by $8 million per month. OD. In approximately 99 months the sales will be $8 million dollars. Choose the correct interpretation of S'(8) -18.88. OA. In approximately 19 months the sales will be increasing by $8 million per month. OB. In approximately 19 months the sales will be $8 million dollars. OC. The total sales 8 months from now will be $18.88 million dollars. OD. In 8 months the sales will be increasing at a rate of $18.88 million per month. 10. For a company that manufactures tennis rackets, the average cost per racket is found to be 1 370 C= +2+x for x 21, where x is the number of rackets produced per hour. X Use the differential to approximate the change in average cost per racket if production is (A) increased from 10 per hour to 14 per hour. (B) increased from 45 per hour to 49 per hour. (A) If production is increased from 10 per hour to 14 per hour the average cost per racket will increase by approximately s per racket. decrease (B) If production is increased from 45 per hour to 49 per hour the average cost per racket will increase by approximately $ per racket. decrease For a company that manufactures tennis rackets, the average cost per racket is found to be C-390 +8+x for x ≥ 1, where x is the number of rackets produced per hour. X Use the differential to approximate the change in average cost per racket if production is (A) increased from 20 per hour to 23 per hour. (B) increased from 30 per hour to 33 per hour. (A) If production is increased from 20 per hour to 23 per hour the average cost per racket will increase by approximately $ per racket. decrease (B) If production is increased from 30 per hour to 33 per hour the average cost per racket will increase by approximately $ per racket. decrease 11. For a company that manufactures tennis rackets, the average cost per racket is found to be 1 380 +9+ for x2 1, where x is the number of rackets produced per hour. X Use the differential to approximate the change in average cost per racket if production is (A) increased from 10 per hour to 16 per hour. (B) increased from 30 per hour to 36 per hour. (A) If production is increased from 10 per hour to 16 per hour the average cost per racket will increase by approximately $ per racket. decrease (B) If production is increased from 30 per hour to 36 per hour the average cost per racket will increase by approximately $ per racket. decrease 1. A company is planning to manufacture snowboards. The fixed costs are $400 per day and total costs are $6200 per day at a daily output of 20 boards. A. Assuming that the total cost per day, C(x), is linearly related to the total output per day, x, write an equation for the cost function. C(x) = B. The average cost per board for an output of x boards is given by C(x)=C(x)/x. Find the average cost function. C(x)= C. Sketch a graph of the average cost function, including any asymptotes, for 1 ≤x≤30. Choose the correct graph below. 500- ELL D. What does the average cost per board tend to as production increases? 500- 30 500- 30 OD. 500 30 ci Most appliance manufacturers produce conventional and energy-efficient models. The energy-efficient models are more expensive to make but cheaper to operate. The costs of purchasing and operating a 25-cubic-foot appliance of each type are given in the table. These costs do not include maintenance charges or changes in electricity prices. Energy-Efficient Model Initial cost Total volume Annual cost of electricity $550 25 ft³ $60 Conventional Model a) Express the total cost C₂(x) and the average cost C₂(x)-Ce(x)/x of purchasing and operating an energy-efficient model for x years. C₂(x) = T.(x) = b) Express the total cost C₂(x) and the average cost C₂(x)=C₂(x)/x of purchasing and operating a conventional model for x years. OA The total costs are the same after OB. The total costs will never be the same. C₂(x)- C.(x)- c) Are the total costs for an energy-efficient model and for a conventional model ever the same? If so, when? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. years. $490 25 ft³ $80 d) Are the average costs for an energy-efficient model and for a conventional model ever the same? If so, when? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. QA. The average costs are the same after years. OB. The average costs will never be the same. e) Find the limit of Ce(x) as x→∞. Dann 2. (cont.) lim C₂(x) = Find the limit of C, (x) as x→∞. lim C₂(x) = Choose the correct implications of the results. OA Over time the average cost of purchasing and operating an energy-efficient model will be more expensive than a conventional model. OB. Over time the average cost of purchasing and operating an energy-efficient model will have the same cost as a conventional model. OC. Over time the average cost of purchasing and operating an energy-efficient model will be cheaper than a conventional model. 3. The revenue (in dollars) from the sale of x car seats for infants is given by the following function. R(x)=24x-0.010x² 0≤x≤2400 (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (B) Use the four-step process to find R'(x). (C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car scats. (Round to one decimal place as needed.) (B) R'(x)= (C) R(1000)- R'(1000) = Interpret these results. Choose the correct answer below. CA. This means that at a production level of 1,000 car seats, the revenue is R'(1000) dollars and is increasing at a rate of R(1000) dollars per seat. OB. This means that at a production level of 1,000 car seats, the revenue is R(1000) dollars and is decreasing at a rate of R'(1000) dollars per seat. OC. This means that at a production level of 1,000 car seats, the revenue is R(1000) dollars and is increasing at a rate of R'(1000) dollars per seat. 4. The total sales of a company (in millions of dollars) t months from now are given by the following formula. S(t) = 9Vt+10 (A) Use the four-step process to find S'(t). (B) Find S(15) and S'(15). (C) Use the results in part (B) to estimate the total sales after 16 months and 17 months. (A) S'(t)- (B) S(15)-(Type an integer or a decimal.) S'(15)= (Type an integer or a decimal.) (C) S(16) (Type an integer or a decimal.) S(17) RS B (Type an integer or a decimal.) 5. The total sales of a company (in millions of dollars) t months from now are given by S(t)-0.031³ +0.41²+71+5. (A) Find S'(t). (B) Find S(7) and S'(7) (to two decimal places). (C) Interpret S(12)=198.44 and S'(12) = 29.56. (A) S'(1) - (B) S(7)= $'(7) - (C) Choose the correct interpretation of S(12)=198.44. CA The total sales 12 months from now will be $198.44 million dollars. OB. In 12 months the sales will be increasing at a rate of $198.44 million per month. Cc. In approximately 198 months the sales will be increasing by $12 million per month. CD. In approximately 198 months the sales will be $12 million dollars. Choose the correct interpretation of S'(12) = 29.56. OA In approximately 30 months the sales will be increasing by $12 million per month. OB. In 12 months the sales will be increasing at a rate of $29.56 million per month. OC. In approximately 30 months the sales will be $12 million dollars. OD. The total sales 12 months from now will be $29.56 million dollars. 6. The total sales of a company (in millions of dollars) t months from now are given by S(t)=0.02t¹ +0.3t²+8t+3. (A) Find S'(t). (B) Find S(3) and S'(3) (to two decimal places). (C) Interpret S(8)=96.44 and S'(8) - 16.64. (A) S'(0) = (B) S(3)- S'(3)= (C) Choose the correct interpretation of S(8)= 96.44. QA The total sales 8 months from now will be $96.44 million dollars. OB. In approximately 96 months the sales will be $8 million dollars. OC. In approximately 96 months the sales will be increasing by $8 million per month. OD. In 8 months the sales will be increasing at a rate of $96.44 million per month. Choose the correct interpretation of S'(8) = 16.64. OA. In 8 months the sales will be increasing at a rate of $16.64 million per month. OB. In approximately 17 months the sales will be $8 million dollars. Oo. The total sales 8 months from now will be $16.64 million dollars. OD. In approximately 17 months the sales will be increasing by $8 million per month. 7. The total sales of a company (in millions of dollars) t months from now are given by S(t)=0.04t² +0.4t² +7t+2. (A) Find S'(t). (B) Find S(5) and S'(5) (to two decimal places). (C) Interpret S(8)=104.08 and S'(8) = 21.08. (A) S'(t) = (B) S(5)- S'(5) - (C) Choose the correct interpretation of S(8) - 104.08. QA In approximately 104 months the sales will be $8 million dollars. OB. The total sales 8 months from now will be $104.08 million dollars. Oc. In approximately 104 months the sales will be increasing by $8 million per month. OD. In 8 months the sales will be increasing at a rate of $104.08 million per month. Choose the correct interpretation of S'(8)-21.08. OA The total sales 8 months from now will be $21.08 million dollars. OB. In approximately 21 months the sales will be $8 million dollars. Oc. In approximately 21 months the sales will be increasing by $8 million per month. QD. In 8 months the sales will be increasing at a rate of $21.08 million per month. po The total sales of a company (in millions of dollars) 1 months from now are given by S(t)=0.04t² +0.2t² +8t+2. (A) Find S'(t). (B) Find S(5) and S'(5) (to two decimal places). (C) Interpret S(8)=99.28 and S'(8) -18.88. (A) S'(1) - (B) S(5)= S'(5)= (C) Choose the correct interpretation of S(8)= 99.28. OA The total sales 8 months from now will be $99.28 million dollars. OB. In 8 months the sales will be increasing at a rate of $99.28 million per month. Oc. In approximately 99 months the sales will be increasing by $8 million per month. OD. In approximately 99 months the sales will be $8 million dollars. Choose the correct interpretation of S'(8) -18.88. OA. In approximately 19 months the sales will be increasing by $8 million per month. OB. In approximately 19 months the sales will be $8 million dollars. OC. The total sales 8 months from now will be $18.88 million dollars. OD. In 8 months the sales will be increasing at a rate of $18.88 million per month. 10. For a company that manufactures tennis rackets, the average cost per racket is found to be 1 370 C= +2+x for x 21, where x is the number of rackets produced per hour. X Use the differential to approximate the change in average cost per racket if production is (A) increased from 10 per hour to 14 per hour. (B) increased from 45 per hour to 49 per hour. (A) If production is increased from 10 per hour to 14 per hour the average cost per racket will increase by approximately s per racket. decrease (B) If production is increased from 45 per hour to 49 per hour the average cost per racket will increase by approximately $ per racket. decrease For a company that manufactures tennis rackets, the average cost per racket is found to be C-390 +8+x for x ≥ 1, where x is the number of rackets produced per hour. X Use the differential to approximate the change in average cost per racket if production is (A) increased from 20 per hour to 23 per hour. (B) increased from 30 per hour to 33 per hour. (A) If production is increased from 20 per hour to 23 per hour the average cost per racket will increase by approximately $ per racket. decrease (B) If production is increased from 30 per hour to 33 per hour the average cost per racket will increase by approximately $ per racket. decrease 11. For a company that manufactures tennis rackets, the average cost per racket is found to be 1 380 +9+ for x2 1, where x is the number of rackets produced per hour. X Use the differential to approximate the change in average cost per racket if production is (A) increased from 10 per hour to 16 per hour. (B) increased from 30 per hour to 36 per hour. (A) If production is increased from 10 per hour to 16 per hour the average cost per racket will increase by approximately $ per racket. decrease (B) If production is increased from 30 per hour to 36 per hour the average cost per racket will increase by approximately $ per racket. decrease
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