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

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3078
On a particular day, three Machines, A, B and C, which produce a....  [#permalink]

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Updated on: 29 Oct 2018, 23:32
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15% (low)

Question Stats:

82% (02:02) correct 18% (02:48) wrong based on 107 sessions

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 To read all our articles:Must read articles to reach Q51 _________________ Originally posted by EgmatQuantExpert on 27 Sep 2018, 03:38. Last edited by EgmatQuantExpert on 29 Oct 2018, 23:32, edited 1 time in total. Manager Joined: 14 Jun 2018 Posts: 217 Re: On a particular day, three Machines, A, B and C, which produce a.... [#permalink] Show Tags 27 Sep 2018, 08:21 1 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 e-GMAT Representative Joined: 04 Jan 2015 Posts: 3078 Re: On a particular day, three Machines, A, B and C, which produce a.... [#permalink] Show Tags 03 Oct 2018, 05:09 1 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.

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