5·The total cost and revenue (in dollars) for the production and sale of x units

Question

5·The total cost and revenue (in dollars) for the production and sale of x units are given, respectively, by: C(x)-32x+36,000 and R(x)-300x 0.03x2 a. Find the profit function P(x). b. Determine the actual cost, revenue, and profit from making and selling 101 units. . Determine the marginal cost, revenue, and profit from making and selling the 101t unit. 6. Suppose 100 items are produced at an average cost of $2 per item. Find the average cost of producing 101 items if the marginal cost to produce the 101t item is (a) $1 (b) S3. You are the manager of a firm that produces slippers that sell for $20 a pair. You are producing 1200 pairs of slippers each month, at an average cost of $2 each. The marginal cost at a production level of 1200 is $3 per pair. a) Are you making or losing money? b) Will increasing production increase or decrease your average cost? Your profit? c) Would you recommend that production be increased or decreased? 7.

Explanation / Answer

5. Profit, P(x)=Revenue,R(x)-Cost ,C(x)

P(x)=300x-0.03x2-32x-36000 =-0.03x2+268x-36000

b. C(101)=32(101)+36000=$39232

R(101)=300(101)-0.03(1012)=$29993.97

P(101)=-0.03(1012)+268(101)-36000=-9238.03

c. C'(x)=32, C'(101)=32

R'(x)=300-0.06x

R'(101)=300-0.06(101)=$293.94

P'(x)=-0.06x+268

P'(102)=-0.06(101)+268=261.94

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