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Solution

As a business entity, the maximization of profit is the primary objective. The possible secondary

objectives are commitments to customers, company reputation and quality of the products.

Profits is revenue minus costs. The revenue is taken from the sales of every single unit of products. The

costs in this case are the costs for material, labor and overhead. We can then modify Table 3 into a table

mentioning the profits for every single unit of each product.

Profits

PRODUCT MATERIAL LABOR OVERHEAD COST SELLING

PRICE

PROFITS

W0075C $33.00 $9.90 $23.10 $66.00 $100.00 $34.00

W0033C $25.00 $7.50 $17.50 $50.00 $80.00 $30.00

W0005X $35.00 $10.5 $24.5 $70.00 $130.00 $60.00

W0007X $75.00 $11.25 $63.75 $150.00 $175.00 $25.00Table 6 Cost, Selling Price and Profits per Unit

Let:

X1 : Number of Product W0075C produced

X2 : Number of Product W0033C produced.

X3 : Number of Product W0005C producedX4 : Number of Product W0007C produced

Then to objective function will be :

MAXIMIZE 34X1 + 30X2 + 60X3 + 25X4 .(1)

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Vivian has given her words to a key customer that they are going to manufacture 600 units of X4 and

150 units of X1. Then we have:

X1 150 (2)

X4 600

For each process, there are boundaries regarding the hour of plant capacity as follow:

PRODUCTS Maximum

Plant

Capacity

(Hours)W0075C W0033C W0005C W0007C

(X1) (X2) (X3) (X4)

DRAWING 1 2 - 1 4,000

EXTRUSION 1 1 4 1 4,200

WINDING 1 3 - - 2,000

PACKAGING 1 - 3 2 2,300

Table 7 Plant Capacity

X1 + 2X2 + X4 4,000

(3)X1 + X2 +4X3 + X4 4,200

X1 + 3X2 2,000

X1 +3X3 + 2X4 2,300

If we assume that Mexicana Wire Works works based on order then :

X1 1,400

X2 250 (4)

X3 1,510

X4 1,116

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Thus, we will have the following model :

Objective : Z: f(X1,X2,X3,X4) = MAX {34X1 + 30X2 + 60X3 + 25X4 }

Constraints: X1 150

X4 600

X1 + 2X2 + X4 4,000

X1 + X2 +4X3 + X4 4,200

X1 + 3X2 2,000

X1 +3X3 + 2X4 2,300

X1 1,400

X2 250

X3 1,510

X4 1,116

X1 , X2 0

By entering the model given above to the POM software table :

Mexicana Wire Works Solution

X1 X2 X3 X4 RHS Dual

Maximize 34 30 60 25

Constraint 1 1 0 0 0 >= 150 0Constraint 2 0 0 0 1 >= 600 -43

Constraint 3 1 2 0 1

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Constraints: X1 150

X4 600

0.5X1 + X2 + 0.5X4 4,000

X1 + X2 +4X3 + X4 4,200X1 + 3X2 2,000

X1 +3X3 + 2X4 2,300

X1 1,400

X2 250

X3 1,510

X4 1,116

X1 , X2 0

The result is given in the following table :

Mexicana Wire Works Solution

X1 X2 X3 X4 RHS Dual

Maximize 30.83 27.6 56.64 21.4

Constraint 1 1 0 0 0 >= 150 0

Constraint 2 0 0 0 1 >= 600 -40.26

Constraint 3 .5 1 0 .5

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product still the same, yet it is not a change for better but for less profit ($53,653) due to no increase in

the pricing but burdened by the increased cost.

Recommendation

It is for maximum profits to produce 1,100 units of W0075C , 250 units of W0033C , and 600 units ofW0007X. Company must turn down the orders to produce 1,510 units of W0005X. It is better for the

company not to increase the number of employee in the drawing department in order to keep the cost

down.