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.