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

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Unformatted text preview: MA. 160 Section 2.6 Worksheet Name ‘1; ~ 65:} ”:21 fem Marginals and Differentials 1. For a certain manufacturer, the daiiy cost in doilars of producing x items is C(x) = 0.905x:3 — 0.5x2 + 28x + 300 . Current daily production is 50 items. a. Use C(x} to calculate C(Sfl} , the current dain cost . b. Use C(x) to calculate C(51) , the daily cost if 51 C (We) : s at; 5065053; 9 5f (5&5? .1 .9 {.590} + 369 items are produces. 3 l I 3’075 C(51); ”wagfiq)"4"5(5U+s§<9($i)+3aa J 3' ‘5’ A; 97:23? ’74,. c. Calculate AC for x = 50 and Ax =1 , the change in d. Find C '(x) , the marginal cost femction. cost when daily production increases from 50 to 51 C" ’(x) 3: 6., 9 15X ‘3; )4 “E, Q i? items. AC = C{x+Ax) - C(x) : C(SO + 1) m C(58) =C(51)«~C(50) m Jase. ere; 10’75: 3/5174; 6. Calculate C(50) , the marginai cost when 50 items f. Use C (x + 1) w C(x) + C '(x) and your answers from are‘produeed daily. 3 parts aandeto approximate C(51) . C (553} S a 0" $650} ""519 +42 3 C (i301 Cé’é‘em}: C(50)“? Cf Wife} ““3 I“. 3/52, 5 £3 Ci‘fiérx‘tw-—_- -'. t \J 20 re e may: $ié"fms~g Maeflaez- ‘94. . M fiat/pt «F; Ala: MW éf flu, {Mm/Wm'des; ”we :5 , 2. The demand function 19(35): p a 65 — J; expresses the market price in dOilfifS in order to sell 3; units of a certain reduct. a. In order to be able to sell 900 units, what should b. How many units will consumers want to buy if the price per item be? the price is set at $40? )0 : g; gr m f; 138%.:er :: ééfflfggmj gig... 3‘2: 3‘5“ €190 4;: gangE __ “‘5‘ ~ .. . w 32‘5”: WW 77‘2“ film WMQK .6143, $3 5:; 2%.. ,3 55“,; V? M12 (few .- . «235‘ = egg: k; c. Find the revenue fimctiou R052). Recall that d. What is the revenue when 900 items are soid? R(x)=x'p ‘2 x (e.-s’wJ7£\ : 4; gm ,. gm Ri‘h‘aa) : sees (g5, 1;;- «fig : $640635") :- 93 j) fig—Ge e. Find the marginal revenue function. f. What is the margins}. revenue when 900 items are twat) :: $.35” ”34' x”??— : (95:, 3 /-— sold. ‘ - 2. EV“). Riééfa-Q):é,f5’w§é?fl¢: 5Z5 figéfigfiwfim m ' , g. Use your answers from parts (1 and f to .‘ he revenue if 901 items are sold, R(?01) “:5 5‘?5?3¢0)+ 3326(990)“; ‘3 315‘¢,_¢;+« 3w :3. 33;) 5-5310 3. Find dy, for each of the following. Note: dy = f '(x)dx 3 - x“ +117 b. y = f0”) m , 3.“ + 4 d? : fixiqflfixifif (Xiyk) (ax) (x31? 14);; c§~ 4-. Use dy to find a decimal approximation of V402 by completing the foilowing. Note: 11y m dy = fwd): = f '(x) Ax of x and Ax in part a , and your approximatien of Ay found in part c to appmximate #402 . Véi’csgl Answers on MYMC ...
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