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# Theory of Constraints

Question:
Taylor company produces two industrial cleansers that use the same liquid chemical input: pocolimpio and maslimpio. Pocolimpio uses two quarts of the chemical for every unit produced, and maslimpio uses five quarts. Currently, Taylor has 6,000 quarts of the material in inventory. All of the material is imported. For the coming year. Taylor plans to import 6,000 quarts to produce 1,000 units of Pocolimpio and 2000 units of Maslimpio. The details of each product's unit contribution margin follows:

Pocolimpio Maslimpio
Selling price \$81 \$139
less variable expenses:
Direct materials 20 50
Direct labor 21 14
Contribution margin 30 60

Taylro company has received word that the source of the material has been shut down by embargo. Consequently, the company will not be able to import the 6000 quarts it planned to use in the coming year's production. There is no other source for the material .

Required

a. compute the total CM the company would earn if the company could import the 6,000 quarts of the material

Pocolimpio: 1,000 units * \$30/unit = \$30,000
Maslimpio: 2,000 units * \$60/unit=\$120,000
Total CM: 30,000+120,000= \$150,000

b. Determine the optimal usage of the company's inventory of 6,000 quarts of the material .
Max:30P + 60M (P: Pocolimpio , M: Maslimpio)

Subj to : 2P +5M &#8804;6,000
P=2
M=5

Solution: M(Maslimpio) &#8804;1199quarts P(Pocolimpio) &#8804;2987quarts

Option:
P:1000 units need 1000 x 2 =2000 quarts
M :2000 units need 2000 * 5 = 10,000 quarts
Total: 12,000 quarts

c. assume that Pocolimpio uses three direct labor hours for every unit produced and that Maslimpio uses two hours. A total of 6,000 direct labor hours is available for the coming year. Formulate the linear programming problem faced by Taylor Company

For direct labor hour
3P+2M &#8804;6,000
P=3
M=2

#### Solution Preview

Taylor company produces two industrial cleansers that use the same liquid chemical input: pocolimpio and maslimpio. Pocolimpio uses two quarts of the chemical for every unit produced, and maslimpio uses five quarts. Currently, Taylor has 6,000 quarts of the material in inventory. All of the material is imported. For the coming year. Taylor plans to import 6,000 quarts to produce 1,000 units of Pocolimpio and 2000 units of Maslimpio. The details of each product's unit contribution margin follows:

Pocolimpio Maslimpio ...

\$2.19