Unformatted text preview: MA 160 Section 2.5 Worksheet Name <3 . C”: W re a
MaximizerMinimum 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?
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v; 4:, (#0 M ﬁfe wakes/d Vzbgeu‘é: c d. What is the maximum proﬁt?
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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.
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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
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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)
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, 2—“. . «p. .. i. . i Z = zfé: . .
55L [til m, x. ,‘Lt o’ex,gm{a_> ,3);ch “3:; :0 AudClif/tmécw $431
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 Fall '10
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