Homework Answers
Marginal cost of 1 tshirt is $4.50
The total cost to print 50 shirts is $275
50*4.5 = 225, so there is an additional cost of $50
Since this is not a marginal cost, it has to be the fixed
cost,
Total Cost = Fixed Cost + (Marginal Cost * Number of items
produced)
TC = FC + MC(X), where X is the number of items
Therefore, the cost function is TC = 50 + 4.5X (the
answer to Part A)
Since her selling price is $9 for tshirt buyers
Profit = SP*X - (TC) = 9X - (50 + 4.5X)
Break even is the point where Profit = 0
0 = 9X - 50 - 4.5X
Solving equation for the value of X
X = 11.11 so she has to sell 12 shirts. (Part
B)
12 * 9 = 108 total revenue by selling 16 tshirts,
therefore
50 + 4.5*12 = 104 total cost
So that's quite close to break even.
Continuing with the question of $900 profit,
900 = 9X - 50 - 4.5X (by substituting in the equation)
solving for X, we get X = 211.11 (Part C)
Therefore, it is expected that she sells 212 shirts, & earns
$900 profit.
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