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 <3 . C”: W 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 refrierator 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 . RU) = x - p(x) b. Find the total proﬁt. P(x) = R(x) — C(x} R(x} = M11250 ‘t‘xl : are 1—» ext rho = {a 3’0 x ex”) _ (grow. 62%; ~- 6. How many refrigerators must the company produce and sell in order to maximize proﬁt? P’OLS .: ”9%”— +295? -—'~ :2. y. +92 52 o :: 4.22 Qezgsro .. , v; 4:, (#0 M ﬁfe wakes/d Vzbgeu‘é: c d. What is the maximum proﬁt? ['7 (”{0} : when» Ag’o(ma.}w gee: a: e. What price per refrigerator must be charged in order to maximize profit? £1?” F a“? 0} M Ce: MVVLﬁbﬂrW/t’vh \ Wm, '1 “from £[email protected],.% x is? x We W2“ em, 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 . . WWW/f Do parts a and b below by carrying out the steps listed: at k a. Suppose that \$48 is available to spend. Find the ‘ 3 b. Suppose the box mus hv volume of 54 " H - dimensions of the box of greatest voiume that can be 3 the dimensions of the least expensive box that can be . . .. .. . .- matted _ . ..... i) What quasatity is t“ be maximized or minimized? 3 i) ‘Nhat questity is to be maximized er minimized? "iﬂahimm ‘ lg” A7259, ﬂex '3 a ii) Give the objective function. C ‘5' 319:1” hi7, “f” Liv/«xi lat: 9X42 ‘fkk iii) Give the constraint equation. W: Jr," " ER ‘ :7 53% I iv) Solve the constraint equation for one of the variables : . in terms of the others. la w 51:? Mime/rue? Meal/W )Gve the obejctlve function. \/ 5 x51 L iii) Give the costratnin eqmatin. I I i H I chai- .—_~: W: it view vat iv) SoEve the constrainteqeatoin for oeeof the variables I 3 in terms of the others. Dev-“i“ if? “i -l‘;’*:x2’+ycl« M [‘wa .; k iv) Exrpess the objective function in ms of one I H I .. variable and determine its domain. Em : (0)003 C(95)” . 14751:“ _yﬂ2(:§2f(g v)Erexpssthebjetiveﬁ1m:tdininterms of one” I variable and determine its domain. 3mm; :.: (:2in V634} : 3:17” ”2/31., X; : vi) Use the ﬁrs or second derivative test to complete vi) Use the ﬁrst or second derWaetestto cometplethe the solution. L soiution. . Q ,4) V’éhl;i3-3v~:o l .Q’Ce):Exrlfbtvl>x'L:fX-—f;f , 2—“. . «p. .. i. . i Z = zfé: . . 55L [til m, x. ,‘Lt o’ex,gm{a_> ,3);ch “3:; :0 AudClif/tmécw \$431 ' f’x‘gu—alh :e (Foals: gear/592.3333; 5:3. w 3, 3.. . '1’ - mitt: 35'. ullb £é3)—81~m33 3514“}939 K3152”? C(59)st ﬂsmmm/Wt 4" ’ x1» J hﬂﬁeﬂﬁiw wvazei'm _7K3_... L—Q’é) dim: “Eh .. . 1’ I..’ szﬂ .. \. I .. ‘7'} ... ,~.A-. , ‘ ‘ﬂt‘a , HM) y .«’M W ...
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