linear function

Question

Soppose that the cost of producing 200bags of yam flour is 18,000 and that the cost increase by 21,000 when 500bags are produced. Determine the linear cost and unit if a price of yam flour is 90 per bag. What will be the profit function and hence the break even point.

Answer 1

Let c be the cost and b be the number of bags. We can write the linear relationship: c=ab+d where a and d are constants.

Now for the figures: 18000=200a+d and 18000+21000=500a+d.

18000=200a+d and 39000=500a+d, so 21000=300a and a=70 (the cost of producing one bag) and 18000-14000=d=39000-35000, so d=4000 (by substitution of a in either equation).

We can now write c=70b+4000. This satisfies the cost side.

On the sales side we have a revenue equation: the revenue r=90b because the price of yam flour is set at 90 a bag. The profit, p, is revenue - cost=r-c=90b-70b-4000=20b-4000. So p=20b-4000.

The break even point is when p=0, when 20b-4000=0, so b=200. When b>200 a profit is made and when b<200 a loss is made.