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On a particular day, three Machines, A, B and C, which produce a....

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On a particular day, three Machines, A, B and C, which produce a....  [#permalink]

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New post 27 Sep 2018, 03:38
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A
B
C
D
E

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  35% (medium)

Question Stats:

73% (02:07) correct 27% (01:39) wrong based on 41 sessions

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On a particular day, three Machines, A, B and C, which produce a product, P, can be used simultaneously, to produce 100 units of P. Each Machine cannot produce more than 40 units in a day. The cost of production per unit of product P by A, B and C are $20, $10 and $5, respectively. What is the ratio of minimum cost to maximum cost incurred, if all 100 units of P are to be produced in a single day?

    A. 1/4
    B. 1/2
    C. 13/20
    D. 10/13
    E. 13/10

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Re: On a particular day, three Machines, A, B and C, which produce a....  [#permalink]

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New post 27 Sep 2018, 08:21
Max units from any machine is 40.
To minimize the cost , maximize a and b = 40*5 + 40*10 + 20*20 = 1000
To maximize the cost , maximize b and c = 20*5 + 40*10 + 4*20 = 1300
Ratio = 10:13
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Re: On a particular day, three Machines, A, B and C, which produce a....  [#permalink]

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New post 03 Oct 2018, 05:09

Solution


Given:
    • On a particular day, machines A, B and C are used to produce 100 units of a product, P
    • Each machine cannot produce more than 40 units, in a day
    • Cost of production per unit of P by machines A, B and C = $20, $10 and $5, respectively

To find:
    • The ratio of minimum cost to maximum cost incurred, if all 100 units of P are to be produced in a single day

Approach and Working:
Minimum Cost:
    • Cost will be minimum, when machine A is used to produce the minimum possible number of units.
      o Hence, A will produce 20 units, and both B and C will produce 40 units each

    • Thus, minimum cost = $20 * 20 + $10 * 40 + $5 * 40 = $1000

Maximum Cost:
    • Cost will be maximum, when machine C is used to produce the minimum possible number of units.
      o Hence, C will produce 20 units, and both A and B will produce 40 units each

    • Thus, maximum cost = $20 * 40 + $10 * 40 + $5 * 20 = $1300

Therefore, ratio of minimum cost to maximum cost incurred = \(\frac{$1000}{$1300} = \frac{10}{13}\)

Hence, the correct answer is Option D.

Answer: D

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Re: On a particular day, three Machines, A, B and C, which produce a.... &nbs [#permalink] 03 Oct 2018, 05:09
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