profit-maximizing activity level

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<br>1. Steam Cleanin Inc. offers professional carpet cleaning to homeowners in Huntsville Alabama. The company is the low-cost provider in this market with fixed costs of $168,750 per year plus variable costs of $10.00 per room of carpet cleaning. Annual demand and marginal revenue for the company are:
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<br>P = $40 - $0.001Q
<br>MR = dTR/dQ = $40 - $0.002Q
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<br>A. Calculate the profit-maximizing activity level.
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<br>To maximize the profit, the company will produce at an output level where MR=MC
<br>The total cost function is
<br>TC=168750+10Q
<br>Then MC dTC/dQ ==10
<br>Let MR=MC: 40 - 0.002Q = 10
<br>Solve for Q*=15000
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<br>B. Calculate the company's optimal profit and return-on-sales levels.
<br>Then Profit(max)=TR-TC=PQ-TC=(40 - 0.001Q)Q - (168750+10Q)
<br>=(40 - 0.001*15000) *15000 - (168750+10*15000) = 56250
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<br>Return on Sales is:
<br>R=Profit/PQ=56250/[(40 - 0.001*15000) *15000] = 0.15
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<br>2. Florida Orange Juice is a product of Florida's Orange Growers' Association. Demand and supply of the product are both highly sensitive to changes in the weather. During hot summer months, demand for orange juice and other beverages grow rapidly. On the other have, hot dry weather has an adverse effect on supply by reducing the size of the orange crop.
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<br>Demand and supply functions for Florida orange juice are as follows:
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<br>Qd = 4,500,000 - 1,200,000P + 2,000,000Ps + 1,500Y + 100,000T
<br>Qs = 8,000,000 + 2,400,000P - 500,000PI - 80,000PK - 120,000T
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<br> Where P is the average price of Florida ($ per case) Ps is the average retail price of canned soda ($ per case), Y is income (GNP in $billions), T is the average daily high temperature (degrees), PI is the average price of unskilled labor ($ per hour), and PK is the average cost of capital (in percent).
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<br>A. When quantity is expressed as a function or price, what are the Florida demand and supply curves if p = $11, Ps = $5, Y = $12,000 billion, T = 75 degrees, and PI = $6, and PK = 12.5%.
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<br>Qd = 4,500,000 - 1,200,000P + ...