Question 1183244
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x = number of units made and sold
x is some positive whole number


Cost equation
C = 2.50x + 4x + 5000
C = 6.50x + 5000
where,
2.50x = cost from just the materials only
4x = cost from just the labor only
5000 = overhead cost


Revenue equation
R = 7.50x
this is the amount of money the company pulls in


Profit equation
P = R - C
P = 7.50x - (6.50x + 5000)
P = 7.50x - 6.50x - 5000
P = x - 5000


We want a positive profit, so we want P > 0
P > 0
x - 5000 > 0
x > 5000


The company must sell more than 5000 units to realise a positive profit
Since x is a whole number, the smallest x can get is x = 5001


Note that if x = 5000, then,
P = x - 5000
P = 5000 - 5000
P = 0
So the company has realized a profit of 0


But if x = 5001, then,
P = x - 5000
P = 5001 - 5000
P = 1
Now the profit is positive


Answer: 5001
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