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AT&T LTE е 70% 9:32 PM 을 webassign.net The total cost C for a manufacturer during a given time period is a function of the nu

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Answer #1

(a)

Total Cost, C = Fixed Cost + Variable Cost = 10N 1200

(b) The price p must be modeled by a linear equation since the decrease in the value of P is constant with the increase in 50 units of N

The points are (200,36) and (250,35.50)

Slope = (35.50-36)/(250-200) = -0.50/50 = -0.01

Using the slope point form, we can write the equation as

p-36一一0.01 (N-200)

p 38-0.01X

Hence the price function is given by p = 38 - 0.01N

(c)

Revenue=Np = N(38 - 0.01N) = 38N - 0.01N^2

(d) The profit function can be determined by subtracting the cost function from the revenue function

P Revenue-Total Cost = (38N-0.01 V2 )-(1200+10N) =-0.01 V2+ 28N-1200

Since the profit contains N^2 term, hence it is a quadratic function

(e)

For break even, the profit must be equal to zero

0.01N2 + 28N 1200-0

Solving the quadratic equation we get

N = 43.53 (smaller value)

N = 2756.47 (larger value)

Note - Post any doubts/queries in comments section.

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