Find the absolute minimums and maximums of the following functions on the given intervals f(x) =...

   

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Find the absolute minimums and maximums of the following functions on the given intervals f(x) = x-6x+5 f(x) = 2x3 1. 2. on [-2,5] on [-2,1] X f(x) = x-3x+5 f(x) = x+1 3. 4. on [-2,1] on [-4,4] 5. You have 120 feet of fencing to construct a pen with 4 equal sized stalls. If the pen is rectangular and shaped like the one below, what are the dimensions of the pen of largest area and what is that area? 6. 7. Suppose you decide to fence the rectangular garden in the corner of your yard. Then two sides of the garden are bounded by the yard fence which is already there, so you only need to use the 80 feet of fencing to enclose the other two sides. What are the dimensions of the new garden of largest area? You have a 10 inch by 15 inch piece of tin which you plan to form into a box (without a top) by cutting a square from each corner and folding up the sides. How much should you cut from each corner so the resulting box has the greatest volume? 10 15 10. A company makes and sells toys. The total cost in dollars for the company to produce an amount q of a cetain toy is given by C(q)=135+2q +0.15q2 Find the quantity that minimizes the average cost for producing that toy. Also find the average cost and the total cost for that quantity. X Launch Meeting - Zoom Launch Meeting - Zoom + S Paused Facebook 'Whiteli... ook 232 / 633 Link for the book | 80% + Chapter 2.4 Applied Optimization The total cost in dollars for Alicia to make q oven mitts is given by (a) What is the fixed cost? C(q) = 64+ 1.5q +0.01q 11. (b) Find a function that gives the marginal cost. 12. (c) Find a function that gives the average cost. (d) Find the quantity that minimizes the average cost. (e) Confirm that the average cost and marginal cost are equal at your answer to part (d). Owners of a car rental company have determined that if they charge customers p dollars per day to rent a car, where 50 p 200, the number of cars n they rent per day can be modeled by the linear function n(p) = 1000 - 5p. If they charge $50 per day or less, they will rent all their cars. If they charge $200 per day or more, they will not rent any cars. Assuming the owners plan to charge customers between $50 per day and $200 per day to rent a car, how much should they charge to maximize their revenue? Consider a pizzeria that sell pizza for a revenue of R(x) = 10x and a 2x + x2 dollars. Link for the book > 32 / 633 |- 80% + 13. $200 per day to rent a car, how much should they charge to maximize their revenue? Consider a pizzeria that sell pizza for a revenue of R(x) = 10x and a cost of C(x) = 2x + x2 dollars. How many pizzas sold maximizes the profit? Go Fly Motors, produces a four-motor airplane. It costs $500 to produce each single aircraft motor and the fixed cost associated with producing the motors is $200 per day. The price function is: p(x) = 800 - - 7.5x 14. Where (p) is the price in dollars at which (x) aircraft motors will be sold. Find: a) The cost function of producing the motors. b) The profit function from producing and selling the motors. c) The quantity of motors that should be produced, and the price at which they should be sold in order to maximize the profit. d) The maximum Profit. Nguyen, Kemp - Long Beach City College - Copyright 2020 231 Next Find the absolute minimums and maximums of the following functions on the given intervals f(x) = x-6x+5 f(x) = 2x3 1. 2. on [-2,5] on [-2,1] X f(x) = x-3x+5 f(x) = x+1 3. 4. on [-2,1] on [-4,4] 5. You have 120 feet of fencing to construct a pen with 4 equal sized stalls. If the pen is rectangular and shaped like the one below, what are the dimensions of the pen of largest area and what is that area? 6. 7. Suppose you decide to fence the rectangular garden in the corner of your yard. Then two sides of the garden are bounded by the yard fence which is already there, so you only need to use the 80 feet of fencing to enclose the other two sides. What are the dimensions of the new garden of largest area? You have a 10 inch by 15 inch piece of tin which you plan to form into a box (without a top) by cutting a square from each corner and folding up the sides. How much should you cut from each corner so the resulting box has the greatest volume? 10 15 10. A company makes and sells toys. The total cost in dollars for the company to produce an amount q of a cetain toy is given by C(q)=135+2q +0.15q2 Find the quantity that minimizes the average cost for producing that toy. Also find the average cost and the total cost for that quantity. X Launch Meeting - Zoom Launch Meeting - Zoom + S Paused Facebook 'Whiteli... ook 232 / 633 Link for the book | 80% + Chapter 2.4 Applied Optimization The total cost in dollars for Alicia to make q oven mitts is given by (a) What is the fixed cost? C(q) = 64+ 1.5q +0.01q 11. (b) Find a function that gives the marginal cost. 12. (c) Find a function that gives the average cost. (d) Find the quantity that minimizes the average cost. (e) Confirm that the average cost and marginal cost are equal at your answer to part (d). Owners of a car rental company have determined that if they charge customers p dollars per day to rent a car, where 50 p 200, the number of cars n they rent per day can be modeled by the linear function n(p) = 1000 - 5p. If they charge $50 per day or less, they will rent all their cars. If they charge $200 per day or more, they will not rent any cars. Assuming the owners plan to charge customers between $50 per day and $200 per day to rent a car, how much should they charge to maximize their revenue? Consider a pizzeria that sell pizza for a revenue of R(x) = 10x and a 2x + x2 dollars. Link for the book > 32 / 633 |- 80% + 13. $200 per day to rent a car, how much should they charge to maximize their revenue? Consider a pizzeria that sell pizza for a revenue of R(x) = 10x and a cost of C(x) = 2x + x2 dollars. How many pizzas sold maximizes the profit? Go Fly Motors, produces a four-motor airplane. It costs $500 to produce each single aircraft motor and the fixed cost associated with producing the motors is $200 per day. The price function is: p(x) = 800 - - 7.5x 14. Where (p) is the price in dollars at which (x) aircraft motors will be sold. Find: a) The cost function of producing the motors. b) The profit function from producing and selling the motors. c) The quantity of motors that should be produced, and the price at which they should be sold in order to maximize the profit. d) The maximum Profit. Nguyen, Kemp - Long Beach City College - Copyright 2020 231 Next