Eastern Chemicals produces 2 types of lubercating fluids used in industrial manu

Question

Eastern Chemicals produces 2 types of lubercating fluids used in industrial manufacturing. both products cost Eastern Chemicls $1 per gallon to produce. Based on an analysis of current inventory levels and outstanding orders for the next month, Eastern Chemicals management specified that at6 least 30 gallons of product one ad at least 20 gallons of product 2 muct be produced during the next 2 weeks. Management also stated that an existing inventory of highly perishable raw m,aterial in the production of both fluids must be used within the next 2 weeks. The current inventory of the perishable raw materials is 80 pounds.    Although more of this raw material can be ordered if necessary, any of the current inventory that is not used within the next 2 weeks will spoil hence the management requirement that at least 80 pounds be used in the next 2 weeks. Furthermore it is known that product 1 requires 1 pound of this perishable raw material per gallon and product 2 requires 2 pounds of the raw material per gallon. Because Eastern Chemicals' objective isa to keep it's production costs at the minimum possible level, the firms management is looking for a minimum cost production plan that uses all 80 pounds of perishable rawe material and provides at least 30 gallons of product 1 and at least 20 gallons of product 2.

What is the minimum cost solution?

Explanation / Answer

Let ‘x’ be the amount of product 1

Let ‘y’ be the amount of product 2

From given Data

x>= 30

y>= 20

As product 1 requires 1 pound of raw material & product 2 requires 2 pounds of raw material

Third constraint become

X+2y>= 80

Solving the above equations

We get infinite region above the line with intersection points (30,25) & (40,40)

Cost for both is $1, so cost will be minimum at 30,25

So total cost will be $55

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