If
C(x) = 17000 + 500x − 1.6x2 + 0.004x3
is the cost function and
p(x) = 1700 − 7x
is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)

Question

If 
C(x) = 17000 + 500x − 1.6x2 + 0.004x3
 is the cost function and 
p(x) = 1700 − 7x
 is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)

Vocaloid · Answer

multiplying the demand function by x will give you the total revenue function

subtracting the cost function from that will give you the profit function

it wants you to maximize the profit so you can just take the derivative of the profit function and solve for x