cost (in dollars) for a run of x hockey jerseys is:
The Revenue function for the number of jerseys x sold is ; R(x) = 90x
The profit function from the sale of x jerseys is ; P(x) = - 0.2x² + 80x - 1500
The number of Jerseys to manufacture in other to make profit = 20
The revenue made is the total amount made from the sale of the hockey jerseys :
Sales price per jersey = $90
Hence, the revenue made, R(x) = 90x
The Cost function, C(x) = C(x) = 1500 + 10x + 0.2x²
Recall :
Profit = Revenue - Cost
Hence,
P(x) = R(x) - C(x)
P(x) = 90 - (0.2x² + 10x + 1500)
P(x) = 90 - 0.2x² - 10x - 1500
P(x) = - 0.2x² + 80x - 1500
To make profit, equate P(x) to 0 ;
0.2x² - 80x + 1500 = 0
Using a quadratic calculator :
x = 380.22 or x = 19.72
Hence, to make a profit, the number of jerseys that must be sold is 20.
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