Question

Cohen Chemicals, Inc. produces two types of photo-developing fluids. The first, a black-and-white picture chemical, costs Cohen $2,500 per ton to produce. The second, a color photo chemical, costs $3,000 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 manger 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 least 60 tons of the photo chemicals in the next month. What is the lowest cost to Cohen Chemicals? post the answers on Excel please. include a photo of the excel spreadsheet

Answer 1

Decision Variables:

Let,

Number of Black and White Picture chemical = x1

Number of Color Photo chemical = x2

Objective Function:

The objective here is to minimize the cost of production.

Cost for Black and White is $2,500 per ton

Cost of Color photo chemical = $3,000 per ton.

So the objective function is:

MINIMIZE 2500*x1 + 3000*x2

Constraints:

At least 30 tons of black and white and 20 tons of color chemical must be produced.

x1 >= 30

x2 >= 20

The total number of chemicals must be at least 60 tons.

x1 + x2 >= 60

Number of chemicals cant be fractional.

x1, x2 = integer

Putting in Excel:

Solver Parameters:

Optimal Solution:

Black and White	Color
x1	x2
40	20

Black and White Chemicals = 40

Color chemicals = 20

Lowest Cost = $160000

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