the manager of a company estimates that it will cost $10,000 to produce 400 unit
ID: 2840393 • Letter: T
Question
the manager of a company estimates that it will cost $10,000 to produce 400 units of her product 1 year from now and that all those unit can then be sold at price $30 per unit. She also estimates that in 1 year, the price will be increasing at rate of 75 cents per unit per month, while the level of production will be decreasing at rate of 2 units per month and the cost will constant.
A, if x is the level of production at time t, where t=0 is 1 year from now, what is the profit P(x)? find the rate at which respect to x. will be profit be increase or decrease at the time?
B, at what rate whill the average profit P(x)/x be changing 1 year from now? will the average profit be increasing or decreasing at the time?
Explanation / Answer
x = 400-2*t (t in months)
t=(x-400)/2
selling rate = 30+0.75*t
production cost is 10,000
total selling amount will be
(400-2t)*(30+0.75*t)
Profit is
a)P(x)= 10,000-(400-2t)*(30+0.75*t) = 10,000-12000+60t-300t+1.5t^2 = 1.5t^2-240t-2000 = 1.5((x-400)/2)^2-240((x-400)/2)-2000
b)P(x)/x =
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