Business mathematics

Question

the profit made by a company when 60 units of its product is sold is r 1 600.00. when 150 units of its products are sold, the profit increases to r 5 200.00. assuming that the profit function is linear and of the form p(u) = a +bu where p is the profit in rands and u is the number of units sold, determine the values of a and b.

Answer 1

5,200 = a + 150b

1,600 = a + 60b

Deducting line 2 from line 1 leaves:

3,600 = 90b

Dividing both sides by 90 leaves

40 = b

Plugging 40 into b in the second formula to find a:

1,600 = a +(60 * 40)

1,600 = a + 2,400

-800 = a

Proving it in the first formula:

5,200 = a + (150*40)

5,200 = a + 6,000

-800 = a

The profit formula is therefore

p(u) = -800 + 40u