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1. Let I represent the units of labor and y the capital invested in a manufacturing process. When 1355:") units are produced, the relationship between labor and capital can be modeled by 1[llil:l:"'7f53r"'25 = 135.540. a. Find the rate of change of capital with respect to units of labor (3?) when labor is 15m units and I the capital invested is l units. Write your answer with correct units. b. As more labor is used. what happens to the available capital? Write your answer in a complete sentence. c. As more capital is used, what happens to the available labor? Write your answer in a complete sentence. 2. A retailer determines that the cost if of ordering and storing x units of a product can be modeled by Z' C:BI+TI iIEZ. The delivery truck can carry at most EDD units per order. Find the order size that will minimize the cost. Write your answer in a complete sentence. 3. A company that manufactures pet toys calculates that its cost if and revenue R can be modeled by x2 C : T'S' + 1.1351: and R : Sx E where x is the number of toys produced in one week. Production during one particular week is EDEN] toys and is increasing at a rate of EEG toys per week. a. Find the rate of change of the cost. Write your answer using a complete sentence with correct units. Find the rate of change of the revenue. Write your answer using a complete sentence with correct units. Find the rate of change of the profit. Write your answer using a complete sentence with correct units. 4. A real estate office handles a SCI-unit apartment complex. When then rent is SEED per month, all units are occupied. For each 54$] increase in rent. however, one unit becomes vacant. Each occupied unit requires approximaterr Slut) per month for service and repairs. a. If there are no increases in rent, what is the profit? b. If the rent is increased to STSD. what is the profit? Let I represent the number of 54C! increases in rent. c. What is the expression that represents the rent? d. What is the expression that represents the number of units occupied? e. What is the revenue function? f. What is the cost function? g. What is the profit function? h. What should the real estate office charge for rent to produce maximize profit and what is the maximum profit? Write vour answer in a complete sentence. 5. The quantity demanded each week x (in units of a hundred) of the Mikado digital camera is related to the unit price p (in dollars) by the demand equation. q = V400 -5p, Ops 80 a. Is the demand elastic or inelastic when p = 40? When p = 80? Write your answers in a complete sentence. b. When does demand have unit elasticity? Write your answer in a complete sentence. c. If the unit price is slightly lowered from $60 will the revenue increase or decrease? Explain using complete sentences. d. If the unit price is slightly increased from $40 will the revenue in increase of decrease? Explain using complete sentences