Question

Cost Minimization

A metal refining plant has decided to install air purifiers to reduce the amount of contamination. Each air purifier costs the plant $ 180,000. The Environmental Protection Agency (EPA) imposes fines of $ 5,000 for each part per million of pollution emitted.

Purifiers	Level of Contamination (Parts per million)	Cost of Purifiers	Cost of Fines	Total Costs
0	150
1	100
2	60
3	30
4	10
5	0

         

1. The optimum level of purifiers to be installed is _____________ and its total cost

                    combined is ___________________________.

Answer 1

Ans:

Total cost = Cost of purifiers + cost of fines

Cost of purifiers = Number of purifiers * $180,000

Cost of fines = level of contamination * $5000.

Calculation of cost of purifiers and cost of fines at each level of contamination.

Purifiers	Level of Contamination (Parts per million)	Cost of Purifiers	Cost of fines	Total costs
0	150	0	$750,000	$750,000
1	100	$180,000	$500,000	$680,000
2	60	$360,000	$300,000	$660,000
3	30	$540,000	$150,000	$690,000
4	10	$720,000	$50,000	$770,000
5	0	$900,000	0	$900,000

Total cost is minimum when 2 purifiers are installed.Hence the optimum level of purifiers to be installed is​ 2 and its combined total cost is $660,000.