Keyser & Acosta Chemical Inc, produces two types of photo-developing fluids. The

Question

Keyser & Acosta Chemical Inc, produces two types of photo-developing fluids. The first, a black anf white picture chemical, costs Cohen $2500 per ton to produce. The second, a color photo chemical costs $3000 per ton. Based on an analysis of current inventory levels and outstanding orders, Cohen's production manager has specified that at least 30 tons of the black and white chemical and at least 20 tons of the color chemical must be produced during the next month. In addition, the manager notes that an existing inventory of a highly perishable raw material needed in both chemicals must be used within 30 days. To avoid wasting the expensive raw material, Cohen must produce a total of at most 60 tons of the photo chemicals in the next month. Let x1=number of tons of black and white picture chemical produced. x2=number of Cohen Chemical problem, we need to solve the formulated minimization. To find a solution to Cohen Chemical problem, we need to solve the formulated minimization problem below: Min 2500x1+3000x2 s.t. x1>30 x2>20 x1+x2<60 x1,x2>0 what are the optimcal value of the decision variables? (PLease show work, i really want to understand)

Explanation / Answer

Ans:

There is infinitely many values of X1, X2 for the optimal value Z = 0, which are contained in the line segment 0 X1 + 0 X2 = 0 that satisfies the constraints of the problem. One is:
X1 = 30
X2 = 20

Ref:Solved using simplex(2-phase method) as below:

The leaving variable is P6 and entering variable is P1.

The leaving variable is P7 and entering variable is P2.

Phase II

There is infinitely many values of X1, X2 for the optimal value Z = 0, which are contained in the line segment 0 X1 + 0 X2 = 0 that satisfies the constraints of the problem. One is:
X1 = 30
X2 = 20

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