The demand function for a certain product is q = -300p + 10,000. The fixed expenses are $500,000 and the variable expenses are $2 per item produced.
a. Express the expense function in terms of q.
b. Use substitution to express the expense function in terms of p.
c. If the price is set at $20, what quantity will be demanded?
d. If price is set at $25, find the demand. Use these numbers in a complete sentence that explains what they mean.
e. If q = 1,000 widgets, find E, the cost (expense) of producing them. Use both numbers in a complete sentence to explain what they mean.
f. If the price is set at p = $15, how much will it cost to produce the correct number of widgets? Use these numbers in a complete sentence to explain what they mean.