Market research for a certain ice cream company indicates that if the price per cup of ice cream is $50.00, the demand will be 1200 cups, whereas if the price is increased to $60.00, the demand will be 1100 cups. (a) If p denotes the price per cup (in dollars) and x denotes the demand for ice cream (in cups), express p as a linear function of x. (b) Determine the revenue function and its domain. (c) Find the marginal revenue at a production level of 200 cups of ice cream. Interpret.
Market research for a certain ice cream company indicates that if the price per cup of ice cream is $50.00, the demand will be 1200 cups, whereas if the price is increased to $60.00, the demand will be 1100 cups.
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(a) If p denotes the price per cup (in dollars) and x denotes the demand for ice cream (in cups), express p as a linear function of x.
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(b) Determine the revenue function and its domain.
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(c) Find the marginal revenue at a production level of 200 cups of ice cream. Interpret.
Now, suppose it is known that the total cost of production of x cups of ice cream is given by C(x) = 3x + 25,500.
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(d) Find the value(s) of x at the break-even points.
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(e) Use marginal analysis to approximate the profit from the sale of the 500th cup of ice
cream. Compare this value with the exact profit from the sale of the 500th cup.
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