Question

7. A furniture company is faced with the following the price-demand function, revenue function, and cost function:
p(x) = 90 - 5x
R(x) = xp(x)
C(x) = 250 + 15x
where p(x) is the price in dollars at which x hundred chairs can be sold and R(x) and C(x) are in thousands of dollars.
(a) Give the revenue R for producing 1200 chairs.
(b) Find the production level that gives the break-even point.
(c) Find the production level that gives the maximum revenue and the maximum profit.

Answer 1

Answer: Given

P=90-5x

R=P*x

C=250+15x

where x is hundred chairs

A) for chairs =1200

so x=1200/100=12

So P=90-5*12=$30

So R=x*P=12*30=$360

B)

for Break even

R=C

P*x=250+15x

(90-5x)*x=250+15x

5x^2-75x+250=0

X^2-15x+50=0

so solving for x we get x=5 or 10

Since breakeven quantity is lowest quantity where R=C

so Breakeven quantity is 500 chairs.

C)

for Maximum revenue

dR/dx=0

R=P*x=(90-5x)*x=90x-5x^2

dR/dx=90-10x

90-10x=0

x=9

So For maximum revenue we have to produce 900 chairs.

For Maximum profit

dR/dx=dC/dx

90-10x=15

x=7.5

So for maximum profit we have to produce 750 chairs.