10.20.Solutions by hand WS 2.6_Page_1

# 10.20.Solutions by hand WS 2.6_Page_1 - MA 160 Section 2.6...

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Unformatted text preview: MA 160 Section 2.6 Worksheet Marginals and Differentials Name éw (fife? the i. For a certain manufacturer, the daily cost in doilars of producing 3; items is C(x) = eoosx3 — 0.5x2 + 2336 + 300 . Current daily production is 50 items. a. Use C(X) to calculate C(50) , the current daily cost . C (We) : l :0 Eé'o’aﬁgm . 5150);; jgéﬁ—a') +309.) '3: 50 '75s 1 b. Use C(x) to calculate C(51) , the daily cost if 51 items are produced. C(51); loci/55(5)): 15(5 ij+2gfs ;)-+Seo e 3/090, 74., c. Calcuiate AC for x = 50 and Ax =1 , the change in cost when daily production increases from 50 to 51 items. AC = C(x+Ax) — C(x) = C(SO -t- l) — C(50) 6. Calculate C (50) the marginal cost when 50 items are produced daily. (1'0: 05—» #01"; (50} “4,0 1,923 1",: \$i5¢5ﬂ YFind C '(x) , the marginal cost ﬁmction. C" ’06.) r: s eigx'ﬁ )4 +359 =C(5i) C(50) = 10%? we» let's: g15:. “7&2 f. Use C(x + 1) e C (x) + C '(x) and your answers from parts a and e to approximate C(51) . “593:5: C(goerzﬁ'xCC5‘oi‘erfé5¢§ (3(513ce’io‘75: PM; 5.9.: \$lei€f¢> 5— . Meme ﬂat; as ., Jam 6 "ff-ALI fCM’t F. m ¢&Wé§« ﬁves (Mme.¢.L image: f) , 2. The demand function Doc) 2 p = 65 —— J; expresses the market price in doilars in order to sell X units of a certain _-reduct. a. In order to be able to sell 900 units, what should the price per item be? ﬁé‘i’eul: £53 my £5 «a 3g: 35’ W 9mm meet nu \$3 ; 2% Mid @6212}? W39, (3. Find the revenue function R(x). Recall that Rm: xrai'x(es ngzé§x_%5l£& b. How many units will consumers want to buy if the price is set at \$49? P : 62 5;” w J; d. What is the revenue when 900 items are sold? Ré‘iéa‘): Cicada (gg'aﬁA ‘3 ‘few iég'wsa) : 6.?0‘0535»): \$57) you e. Find the marginal revenue function. nit») : new ”if x ”a : g. Use your answers from partsdaud f to '- R(?al)ﬁf fié‘?wo)+ﬁ (9’99) l 3! 56.262wa 1:, 33]) 3&0 f. What is the marginal revenue when 900 items are sold. R ’{90»¢:2.): £25“ 5* ea; 1.” £2 «:3 “géﬁagﬁwmw mﬂ 7 ...
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