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# A certain clothing manufacturer makes only two types of

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A certain clothing manufacturer makes only two types of [#permalink]

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13 Mar 2005, 23:13
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Difficulty:

(N/A)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 4 sessions

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A certain clothing manufacturer makes only two types of men's blazer: cashmere and mohair. Each cashmere blazer requires 4 hours of cutting and 6 hours of sewing. Each mohair blazer requires 4 hours of cutting and 2 hours of sewing. The profit on each cashmere blazer is $40 and the profit on each mohair blazer is$35. How many of each type of blazer should the manufacturer produce each week in order to maximize its potential weekly profit on blazers?

1) The company can afford a maximum of 200 hours of cutting per week and 200 hours of sewing per week.

2) The wholesale price of cashmere cloth is twice that of mohair cloth.
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14 Mar 2005, 00:41
A.

Lets say X type1 and Y type2.

1. 4X + 4Y <= 200
X + Y <= 50

2. 2X + 6Y <= 200
X + 3Y <= 100

2Y <= 50
Y <= 25
X <= 25

Total profit, 40X + 35Y, is maximum when both X = Y = 25.
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14 Mar 2005, 13:07
I say it is E will explain later if i am right
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14 Mar 2005, 14:43
A

keep in mind that for 2) we already know the profit so the cost of the cloth is useless. easy elimination.
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14 Mar 2005, 21:49
Tough one ywilfred

I would go for E
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15 Mar 2005, 11:17
I'll leave this problem up for another day to see if anyone else wants to have a go. After that, i'll release the OA
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16 Mar 2005, 04:56
OA is A
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16 Mar 2005, 18:01
Great problem ywilfred
I am gonna have a look on mckenna post to see how he found it out...
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18 Apr 2005, 13:59
i have taken operations maagment class ,,,,this is a linear programing topic,,,,,,,,,,,i would sujjest tht make it a thumb rule tht...............if ther are two conditions and 1 maximizing ful eqution

conditions 4b+6w<200
6b+2W<200
maxim function 40x+35y.........

the points of maximization can be calculated...........

just remeber this and follow yr options.......

all the best!
c u at harward
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i hate when people do'nt post the OA, it leaves in guessing!!!!

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18 Apr 2005, 22:18
ywilfred wrote:
two types of men's blazer: cashmere and mohair. Each cashmere blazer requires 4 hours of cutting and 6 hours of sewing. Each mohair blazer requires 4 hours of cutting and 2 hours of sewing. The profit on each cashmere blazer is $40 and the profit on each mohair blazer is$35.
1) The company can afford a maximum of 200 hours of cutting per week and 200 hours of sewing per week.
2) The wholesale price of cashmere is twice that of mohair.

nice problem, ywilfred. agree with A. time taken to make per blazer and profit per blazer are given. so A is sufficient as you have already provided the information, however i havenot solved the problem.
Re: DS   [#permalink] 18 Apr 2005, 22:18
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