Question

The profit made by a company when 60 units of its product is sold is R1600.00. When 150 units of its product is sold, the profit increases to R5200. Assuming that the profit function is linear and of the form
P(u) =a+but where Possible is the profit in Rands and u is the number of units sold, determine the:
1. Value of a and b
2. Break-even level
3. Number of units that need to be sold to realise a profit of R12 000. 00.

Answer 1

Answer:

1) a = -800,  b = 40

2) break even level is 40 units

3) to make a profit of R12000, 280 units must be sold.

Step-by-step explanation:

The given equation for profit is,

P = a + bu

1) from the conditions given above we can form two different equations,

1600 = a + 60b..................eqn1

5200 = a + 150b..............eqn2

subtracting equation1 from eqn2 we get,

3600 = 90b

=> b = 3600/90 = 40

putting the value of b in eqn1 we get,

1600 = a+ 60x40

=> a = -800

2) Break-even level is defined as the number of units to be sold for no profit or no loss, hence

P = a + bu

=> 0 = -800 + 40u

=> 40u = 800

=> u = 800/40 = 20

Hence break even level is 40 units

3) To make a profit of 12000

P = a + bu

=> 12000 = -800 + 40u

=> 40u = 11200

=> u = 11200/40 = 280 units

Hence to make a profit of R12000, 280 units must be sold.