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The Audubon Society at Enormous State University (ESU) is planning its annual fund-raising "Eatathon." The society will charge students $1.10 per serving of pasta. The society estimates that the total cost of producing x servings of pasta at the event will be C(x) = 370 + 0.10x + 0.002x2 dollars. (a) Calculate the marginal revenue R'(x) and profit P'(x) functions. HINT [See Example 2.]

Respuesta :

Answer:

a) R'(x) = $1.1

b) P'(x) = 1 - 0.004x

Explanation:

Given:

Charges for per serving of pasta = $1.10

let the total number of pasta served be 'x'

Therefore,

Revenue, R(x) = $1.1x

a) Now,

Marginal revenue, R'(x) = [tex]\frac{d(1.1x)}{dx}[/tex]

= $1.1

b) cost function , C(x) = 370 + 0.10x + 0.002x²

also,

Profit = Revenue - Cost

thus,

P(x) = R(x) - C(x)

= $1.1x - (310 + 0.10x + 0.002x²)

Now,

Marginal profit, P'(x) = [tex]\frac{d(1.1x - (370 + 0.10x + 0.002x^2))}{dx}[/tex]

or

= 1.1 - 0 - 0.10 - 2(0.002x)

or

P'(x) = 1 - 0.004x

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