Question

1. At a price $p per unit, the marketing department at a local company esti- mates that the weekly costs are given by the equation C = 2p + 12

and the revenue is given by the equation R = 10p ? p2

(a) The company makes a profit when the revenue is bigger than the costs.

At what prices will the company have a profit?

(b) The company will have a loss if the costs are greater than the revenue. At what prices will the company have a loss?

Hey guys i am having troblem to find out the solation, could you giys help me?

Thanks

Answer 1

weekly cost are given by the equation

C=2p+12.........(1)

and the revenue is given by the equation

R=10p-p².........(2)

part(a) in this part we have to find the price at which the company have a profit

and as we know that company makes a profit when revenue is bigger than costs

it means we get profit when R>C

i.e 10p-p²>2p+12

p²+2p-10p+12<0

p²-8p+12<0

(p-2)(p-6)<0

if p-2<0 then p-6>0 imply p<2 and p>6 which is not possible

and if p-2>0 then p-6<0 then p>2 and p<6 which is the correct answer

part(b) here we have to find the price at which company have a loss

loss will attained if C>R

means 2p+12>10p-p²

p²+2p+12-10p>0

p²-8p+12>0

(p-2)(p-6)>0

then if p-2>0 then p-6>0 imply p>2 and p>6

if p-2<0 then p-6<0 imply p<2 and p<6