A contractor wishes to determine a suitable combination of manual labour and machine work for the excavation of a multistory construction. For every cubic meter of excavation, 3 man-hours are needed; or 0.2 machine-hour. Costs involved are Rs. 20 per man-hour and Rs. 500 per machine-hour. The total quantity of excavation is estimated to be 4,000 cubic meter. The optimal quantity of excavation to be done manually for minimum total cost will be?
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Answers
Given : cost for manual labour and machine work for the excavation of a multistory construction
To find : optimal quantity of excavation to be done manually for minimum total cost will be
Solution:
For every cubic meter of excavation
Man hours required = 3
Cost per man hour = Rs 20
Cost for manual work for every cubic meter of excavation = 3 * 20 = Rs 60
For every cubic meter of excavation
Machine hours required = 0.2
Cost per machine hour = Rs 500
Cost for machine work for every cubic meter of excavation = 0.2 * 500 = Rs 100
60 < 100
Cost for manual work for every cubic meter of excavation < Cost for machine work for every cubic meter of excavation
as no other constraints are given
like days for completion of work
availability of man hrs or machine hrs
so only man hrs to be used for minimum cost as manual cost is lower
Cost = 4000 * 60
= 240000 Rs
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