Question 1183244: To produce 1 unit of a new product, a company determines that the cost for material is N2.50 per unit and the cost of labour is N4 per unit. The constant overhead cost is N5, 000. If the cost to a wholesaler is N7.50 per unit, determine the least number of units that must be sold by the company to realise a positive profit.
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
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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