Please answer all parts and show all work. Especially part c-e 1. The managers o

Question

Please answer all parts and show all work. Especially part c-e 1. The managers of Windolux, Inc. have modeled some cost data and the cost (in dollars) is given by the function: 49.6032 C(x)-0.0146x-0.7823x+46.9125+ where x is number of windows produced dollars Windolux sells its windows for $175 each. (You may assume that every window made will be sold). a) Write the formula for the revenue when Windolux is producing x windows b) Write the formula for the profit when Windolux is producing x windows e) What is the profit when Windolux is producing 80 windows? Write the conclusion in complete sentence. d) Find the marginal profit. e) How rapidly is profit from the sale of a window changing when 80 windows are produced? Interpret your answer

Explanation / Answer

a). Formula for revenue = $175 x

b). Formula for profit = Revenue - Cost
= $175x - (0.0146x^2 - 0.7823x + 46.9125 + 49.6032/x)

c). Profit when 80 windows are produced :-
= $175 * 80 - (0.0146* (80)^2 - 0.7823*80 + 46.9125 + 49.6032/80)
= $13921.61
It means profit earned by the company by selling 80 windows is $13921.61

d). Marginal profit is the profit earned by producing one additional unit.
For that we have to calculate profit for 81 units.
= $175 * 81 - (0.0146* (81)^2 - 0.7823*81 + 46.9125 + 49.6032/81)
= 14095.05

Marginal profit = Profit at 81 units - Profit at 80 units
= $14095.05 - $13921.61
= $173.44

e).( I don't clearly understand this part, what it exactly wants because there is nothing for the comparison on which basis I can see change in profit, even then I'll explain on the basis of last part.)
Profit of the company is changing by $173.44 per unit when it changes its production as we can see in last part. Increase in profit due to increase in units from 80 to 81 results in additional profit of $173.44 which is the marginal profit by selling one additional unit of window.

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