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A manufacturer wants to produce x balls and y boxes. Resource constrai

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A manufacturer wants to produce x balls and y boxes. Resource constrai  [#permalink]

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New post Updated on: 27 Apr 2020, 17:40
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Question Stats:

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\(7x + 6y \leq 38,000\)

\(4x + 5y \leq 28,000\)

A manufacturer wants to produce x balls and y boxes. Resource constraints require that x and y satisfy the inequalities shown. What is the maximum number of balls and boxes combined that can be produced given the resource constraints?

A.  5,000
B.  6,000
C.  7,000
D.  8,000
E. 10,000

PS30421.02

Originally posted by parkhydel on 27 Apr 2020, 14:27.
Last edited by chetan2u on 27 Apr 2020, 17:40, edited 1 time in total.
Corrected the Q
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Re: A manufacturer wants to produce x balls and y boxes. Resource constrai  [#permalink]

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New post 27 Apr 2020, 17:39
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parkhydel wrote:
\(7x + 6y \leq 38,00\)

\(4x + 5y \leq 28,00\)

A manufacturer wants to produce x balls and y boxes. Resource constraints require that x and y satisfy the inequalities shown. What is the maximum number of balls and boxes combined that can be produced given the resource constraints?

A.  5,000
B.  6,000
C.  7,000
D.  8,000
E. 10,000

PS30421.02



I believe the equations must be talking of 28,000 and 38000 and not 3800 and 2800 because we have a comma after sets of 3 digit in GMAT, and also answers are in 1000s.

\(7x + 6y \leq 38,000\)

\(4x + 5y \leq 28,000\)

Add both the inequalities..
\(7x+6y+4x=5y\leq{38000+28000}\)

\(11x+11y\leq{66000}....x+y\leq{6000}\)

B
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Re: A manufacturer wants to produce x balls and y boxes. Resource constrai  [#permalink]

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New post 10 May 2020, 15:12
I was thinking about how to do it fast.

We simply have to look at the options.

According to the second expression, the sum of x and y should be multiplied on at least 4.

C, D and E give us a result that is more than 28k. As a result, the only two options are A and B. We choose the B because we are looking for Max.

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Re: A manufacturer wants to produce x balls and y boxes. Resource constrai  [#permalink]

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New post 02 Jun 2020, 07:45
Since we have to produce both balls and boxes to a maximum capacity, we can't neglect any of the terms.

Constraint 1:

we need to have a value such that 7x+6y<=38.
2 Possible situations are 7*1 + 6*5 <=38 or 7*4+6*1 <= 38
So, according to this equation, we can produce 6000 (1000+5000) or 5000 (4000+1000)

Constraint 2
Similarly, we have 2 possibilities to get close to 28.
4*2+5*4 <= 28 or 4*5+5*1 <= 28
According to this equation, we can produce 6000 (2000+4000) or 6000 (5000+1000)

Combining both the constraints, the maximum we can produce is 6000. Answer is B
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Re: A manufacturer wants to produce x balls and y boxes. Resource constrai  [#permalink]

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New post 02 Jun 2020, 08:45
parkhydel wrote:
\(7x + 6y \leq 38,000\)

\(4x + 5y \leq 28,000\)

A manufacturer wants to produce x balls and y boxes. Resource constraints require that x and y satisfy the inequalities shown. What is the maximum number of balls and boxes combined that can be produced given the resource constraints?

A.  5,000
B.  6,000
C.  7,000
D.  8,000
E. 10,000

PS30421.02


\(7x + 6y \leq 38,000\)---------------->(I)
\(4x + 5y \leq 28,000\)---------------->(II)

(I) + (II) => \(11x + 11y \leq 66000\) Or, \(x + y \leq 6000\), Answer must be (B)
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Re: A manufacturer wants to produce x balls and y boxes. Resource constrai   [#permalink] 02 Jun 2020, 08:45

A manufacturer wants to produce x balls and y boxes. Resource constrai

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