Suppose that for a company manufacturing calculators, the cost, revenue, and pro

Question

Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are
given by
C = 72, 000 + 60x
R = 200x ?x^2/30

P = R ? C

where the production output in 1 week is x calculators. If production is increasing at a rate of
500 calculators per week when production output is 1, 500 calculators, find the rate of increase or
decrease in (A) Cost (B) Revenue (C) Profit.

Given the price-demand equation
p + 0.01x = 50

1. Express the demand x as a function of the price p.

2. Find the elasticity of demand, E(p).

3. What is the elasticity of demand when p = $10? If this price is decreased by 5%, what is the
approximate change in demand?

4. What is the elasticity of demand when p = $45? If this price is decreased by 5%, what is the
approximate change in demand?

5. What is the elasticity of demand when p = $25? If this price is decreased by 5%, what is the
approximate change in demand?

Explanation / Answer

To find rates of change you need to take the derivative with respect to x.

dC/dx = 30*dx = 30*500 = 15,000

dR/dx = 300dx - (2/30)xdx
= 300*500 - (2/30)*6000*500
= 150,000 - 400*500 = 150,000 - 200,000 = -50,000

dP/dx = dR/dx - dC/dx = -50,000 -15,000 = -65,000

Rate of change in cost=marginal cost

=C '(x)= 40

Rate of change in Revenue=marginal revenue

=R '(x)= -2x/30= -x/15

Profit=R(x)- C(x)

P(x)=(9000+40x) -(400-(x^2/30))

=x^2/30 +40x +8,600

Rate of change in profit=marginal profit

=p '(x)=2x/30 + 40= x/15+40

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