Question

# Cost, revenue, and profit are in dollars and x is the number of units. Suppose that...

Cost, revenue, and profit are in dollars and x is the number of units.

Suppose that the total revenue function is given by

R(x) = 48x

and that the total cost function is given by

C(x) = 70 + 29x + 0.1x2.

(a) Find P(100).
P(100) =

(b) Find the marginal profit function MP.
MP =

(c) Find MP at x = 100.
MP(100) =

Explain what it predicts.

At x = 100, MP(100) predicts that cost will increase by |MP(100)| dollars. At x = 100, MP(100) predicts that profit will decrease by |MP(100)| dollars.     At x = 100, MP(100) predicts that cost will decrease by |MP(100)| dollars. At x = 100, MP(100) predicts that profit will increase by |MP(100)| dollars.

(d) Find P(101) − P(100).
\$

Explain what this value represents.

The sale of the 100th unit will increase profit by |P(101) − P(100)| dollars. The sale of the 101st unit will increase profit by |P(101) − P(100)| dollars.     The sale of the 100th unit will decrease profit by |P(101) − P(100)| dollars. The sale of the 101st unit will decrease profit by |P(101) − P(100)| dollars.

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