Answer to Question #87382 in Calculus for Mnyamezeli Luthuli

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

Answer 1

$$P(u)=a+bu$$

$$P(60)=a+b(60)=R\ 1 600.00$$

$$P(150)=a+b(150)=R\ 5 200.00$$

$$90b=R\ 3600.00 \Rarr b=R\ 40.00$$

$$a=R\ 1 600.00-R\ 40.00(60)=-R\ 800.00$$

$$P(u)=-800+40u$$

Break-even level: total profit is zero

$$P(u)=0 \Rarr -800+40u=0, u=20$$

Number of units that need to be sold to realise a profit of R 12 000.00.

$$-800+40u=R\ 12 000.00$$

$$u=280$$