Name:
SUMMERII, 2014
MATH 142:203
QUIZ - 2
• This is a group quiz, open notes, open book. Due Monday, July 14, at the beginning
of lecture.
• Read each question carefully, answer each question completely, box your answers.
• Show all of your work; no credit will be given for unsupported answers.
• Initial your name on each problem you contribute ideas or solutions to the group.
It costs a company $500 to produce 10 table lamps beside a fixed monthly cost of $250. If the price of
each table lamp is $90, the company can sell 20 table lamps. If the price of each table lamp is $70, the
company can sell 30 table lamps. Find:
a. (2.5 pts) The linear cost function
500=m10
m=50
C(x) = 50x + 250.
b. (2.5 pts) The linear price-demand equation
p(x) = −cx + d
90 = −c20 + d
70 = −c30 + d
So, 20 = 10c.
c=2
70 = −2(30) + d
d = 130
p(x) = −2x + 130.
c. (2.5 pts) The profit function
Revenue function: R(x) = xp(x) = x(−2x + 130) = −2x2 + 130x.
Profit function: P (x) = R(x) − C(x) = (−2x2 + 130x) − (50x + 250) = −2x2 + 80x − 250.
d. (2.5 pts) The price per table lamp at maximum profit
The profit attains its maximum at
x=
−80
= 20.
2(−2)
Hence, the price per table lamp at maximum profit is
p(x) = −2x + 130 = −2(20) + 130 = 90.