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

Question

Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the total revenue function for a product is R(x) - 35x and that the total cost function is C(x) 1900+ 15x+ 0.01x2, (a) Find the profit from the production and sale of 500 units. $ 5600 (b) Find the marginal profit function. (c) Find MP at x = 500. MP- Explain what it predicts. The total profit will increaseby approximately $ on the sale of the next (501st) unit. (d) Find P(501)- P(soo). Explain what this value represents. O This is the total profit for 501 units O This is the actual revenue on the sale of the 501st unit. This is the actual profit on the sale of the 501st unit. O This is the actual cost of the 501st unit. O This is the total cost of 501 units. Need Help? hen s-of-Malfi-...pdf

Explanation / Answer

(a)

profit function,P(x) =R(x)-C(x)

=>P(x) =(35x)-(1900+15x+0.01x2)

=>P(x) =-1900+20x-0.01x2

when x =500

P(500) =-1900 +20*500 -0.01*5002

=>P(500) =5600

profit from the production and sale of 500 units is $ 5600

(b)

marginal profit function,MP= P'(x)

MP= -0 +20*1 -0.01*2x

MP= 20 -0.02x

(c)

at x=500

MP=20 -0.02*500

MP=20-10

MP=10

The total profit will increase by approximately $ 10 on the sale of the next (501st) units

(d)

P(501)-P(500) =[-1900 +20*501 -0.01*5012]-[-1900 +20*500 -0.01*5002]

=>P(501)-P(500) =5609.99-5600

=>P(501)-P(500) = $ 9.99

this value represents

this is the actual profit on the sale of the 501st unit

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