10.13.Solutions by hand WS 2.5_Page_1

10.13.Solutions by hand WS 2.5_Page_1 - MA 160 Section 2.5...

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Unformatted text preview: MA 160 Section 2.5 Worksheet Name £2 . é: Uy’ re a Maximizer-Minimum Problems; Business and Economics Applications 1. A company is marketing a new refrigerator and it determines that in order to sell x refrigerators, the price per refiierator must be p m 280 -— 0.4x. The cost of producing x refrierators is given by C(X) = 5000+0.6x2 a. Find the total revenue , R(x) = x - p(x) b. Find the total profit. P(x) = R(x) — C(x} R(x} = X ($80“, ‘in 3 £30 an é’x‘)‘ P(x) = {a 3’0 'X—W ‘9" 75’} ’ (Ewes v 62;” “ o. How many refrigerators must the company produce and sell in order to maximize profit? P’OLS .: ”9%”— +295? -—'~ :2. y. +542 52 o :: 4.22 sisszgvgo .. . i6; 4:, (#0 m7 fife wakes/é Vzogeuil: I, d. What is the maximum profit? ['7 (”{0} : Demon» newest“ sea a: e. What price per refrigerator must be charged in order to maximize profit? 1&9” F a“? a} M Ce: XVI/Lfibflrwmh \ Wm, '1 “from BMW‘A K 1:113}, ‘f; (Ta—mfié W“ rein h 2. A closed reotanguiar box with a square base is to be constructed using two different types of wood. The top is made of wood costing $3 per square foot and _ the remainder is made of wood costing $1 per square foot. In the “box” on the . right, draw a picture and label the sides with variables. h . . mow/f Do parts a and b below by carrying out the steps listed: a k a. Suppose that $48 is available to spend. Find the ‘ 3 b. Suppose the box mus hv vuolme of 54 " H - dimensions of the box of greatest voiurne that can be 3 the dimensions of the Eeast expensive box that can be moot. . . .. .. . .- meted _ . ..... i) What quantity is t“ be maximized or minimized? 3 i) What quantity is to be maximized er minimized? "iflahimm ‘ lg” $7259, from, '3 a ii) Give the objective function. C ‘5' 319:1” hi7, “i” Liv/«xi hi: 9X42 ‘fkk iii) Give the constraint equation. W: Jr," " PC" ‘ :7 53% I iv) Solve the consrraint equation for one of the variables : . in terms ofthe others. lo w 51:? Mime/rue? Mega/W ) Give the obejctive in. ' \/ 5 x51 L iii) Give the costranint equation. I i I. I I chai- .—_~: as“: a mega; ah iv) Soive the ccwttnrainerpztoain for oneof the variables I 3 in terms ofthe others. Dev-“i“ if} a”? .i‘r13x2-Léka M [‘an .: k iv) Exrpess the objective function in ms of one I H I .. variable and determine its domain. Em : ( 01,603 C(x)” . ‘9. 45"1“ _’K2(i'—;2féy v) Wisp the objetive Winin terms of one I variable and determine its domain. 3mm; :.: (:2in 'Vék‘.) : s17” rig"), K. : vi) Use the firs or second derivative test to complete vi) Use the first or second derWaetestto cometplethe the solution. » soiution. . he {'43 V’énl;i3e3w:o l .C’Zjh):é’xrltépwa'L35’x—W , 2—1., , . «p. w ... Z = at!» W . , . 5:; l1 m. 24.. 4Q emx,gm{0)_5 5’25”) -le ~63 Ari-«dddghgrfiéguha xii-4i ' f’x‘gwata :e (IVs-ls: Shampoo”: 59;. W... 3, 3.. . '1’ - mile: 35'. ullb £é3)—81~_§3..3914§0 Eta-:42"? 6(3):;35» flammm/Wt 4" ’ KT; J hflfihflfiiw yrs/62am _7K3_... L—Q’é) dim: “33% .. . 1’ I..’ szfl .. \. I .. .7? ... ,~.A-. , ‘ ‘flt‘a , HM) y .«’M W ...
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