3/10/2018 Math 1306 Homework 4.5 .-114.28 pointsSApCalcBr 3.2.019. A manufacture

Question

3/10/2018 Math 1306 Homework 4.5 .-114.28 pointsSApCalcBr 3.2.019. A manufacturer of power supplies estimates that it will incur a total cost of C(a) - 2700 +Sq+0.006q dollars when producing q power supplies, and it will collect A(q)-16q-0.00Sq2 dollars in revenue. (a) write a function for the profit P the manufacturer can expect after produclog q power supplies P(a) (b) Find the marginal cost and marginal revenue functions. marginal cost marginal revenue (c) How many power supplies should the manufacturer produce in order to maximize profit? power supplies

Explanation / Answer

a. Profit=Revenue - cost

P(q)=R(q)-C(q)

P(q)=16q-0.005q2-2700-5q-0.006q2

P(q) = -0.011q2+11q -2700

b. Marginal cost, C'(q)=5+0.012q

Marginal revenue, R'(q)=16-0.010q

c.P'(q)=-0.022q +11

P'(q)=0

0.022q=11

q=11/0.022 =500

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