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The profit made as a function of x ;
Let :
Number of units produced = x
Profit per unit = $3
Fixed cost = $17,000
Total profit made : Revenue - Cost of production
Profit, P(x) = (profit per unit × number of units) - Fixed cost
Profit, P(x) = 3x - 17,000
B.)
When x = 20,000
P(20000) = 3(20000) - 17,000
Profit = 60000 - 17,000
Profit = 43,000
When x = 5000
P(5000) = 3(5000) - 17,000
Profit = 15000 - 17,000
Profit = - 2000
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The total profit as a function of x is P(x) = 3x - 17,000
(A) The profit is $43,000
(B) The loss is $2,000
The given parameters;
The following equations will be set up as follows;
Total cost price = 17,000 + x(y)
Total selling price = x(y + 3)
The total profit as a function of x is calculated as;
total Profit = total selling price - total cost price
total Profit = x(y+3) - 17,000 - xy
total Profit = xy + 3x - 17,000 - xy
total Profit = 3x - 17,000
P(x) = 3x - 17,000
(A) The profit or loss when x = 20,000 units are produced;
P(20,000) = 3(20,000) - 17,000
P(20,000) = 60,000 - 17,000
P(20,000) = $43,000
The profit is $43,000
(B) The profit or loss when x = 5,000 units are produced;
P(5,000) = 3(5,000) - 17,000
P(5,000) = 15,000 - 17,000
P(5,000) = - $2,000
The loss is $2,000
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