**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?
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i6; 4:, (#0 m7 ﬁfe wakes/é Vzogeuil: I, d. What is the maximum proﬁt?
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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.
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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 . , .
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