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Meteor Tie Company produces ties from fabric according to Q = 10 + 4 F – (1/3) F 3. If fabric is free and ties sell for $20, what is Meteor’s optimal usage of fabric?
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7 votes
7 votes
Meteor Tie Company produces ties from fabric according to Q = 10 + 4 F – (1/3) F 3. If fabric is free and ties sell for $20, what is Meteor’s optimal usage of fabric?

User Loyalflow
by
2.7k points

1 Answer

10 votes
10 votes

Answer:

The optimal usage of fabric = 2

Step-by-step explanation:

Given the quantity, Q = 10 + 4F - (1/3) F^3

Selling price = $20

Profit = TR - TC

There is no variable cost and let the fixed cost is constant G.

Profit = PQ - G

Profit = 20(10 + 4F − (1/3)F^3)) - G = 0

Now take the first order derivative:

d(profit) / dF = 0

20(4 - F^2) = 0

F = 2

Therefore the optimal usage of fabric = 2

User ValYouW
by
3.2k points
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