An ice cream company finds that at a price of $4.00 for each pint, they can sell 4000 pints of ice cream per day. For every $0.25 decrease in price, daily demand increases by 200 units. The company’s cost function is C(q)=0.01q2-90q+211600, where C represents their daily costs (in dollars), and q is the number of pints sold per day. a)Find the demand function q(p). b) Find the revenue function R(q). Hint: first you will need to solve for p in terms of q from the demand function.) c) How many pints should the company sell per day if they want to maximize their revenue? d) what price should the company charge for each pint if they want to maximize their revenue? e)Use the criteria MC(q)=MR(q) to determine how many pints the company should sell per day if they want to maximize their profit. f)What is the maximum profit the company can earn per day? g)Find the average cost function. h)How many pints should the company sell per day if they want to minimize their average cost? What do you notice about the marginal cost and average cost at the production level found in (h)? Explain why this makes sense.
*** Please answer e, f, g,h**
An ice cream company finds that at a price of $4.00 for each pint, they can sell 4000 pints of ice cream per day. For every $0.25 decrease in price, daily demand increases by 200 units. The company’s cost function is C(q)=0.01q2-90q+211600, where C represents their daily costs (in dollars), and q is the number of pints sold per day.
a)Find the demand function q(p).
b) Find the revenue function R(q). Hint: first you will need to solve for p in terms of q from the demand function.)
c) How many pints should the company sell per day if they want to maximize their revenue?
d) what price should the company charge for each pint if they want to maximize their revenue?
e)Use the criteria MC(q)=MR(q) to determine how many pints the company should sell per day if they want to maximize their profit.
f)What is the maximum profit the company can earn per day?
g)Find the average cost function.
h)How many pints should the company sell per day if they want to minimize their average cost? What do you notice about the marginal cost and average cost at the production level found in (h)? Explain why this makes sense.
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