Question

In: Operations Management

a) A chemical manufacturer processes two chemicals, Arkon and Zenon, in varying proportions to produce three...

a) A chemical manufacturer processes two chemicals, Arkon and Zenon, in varying proportions to produce three products, A, B, and C. He wishes to produce at least 150 units of A, 200 units of B, and 60 units of C. Each ton of Arkon yields 3 of A, 5 of B and 3 of C. Each ton of Zenon yields 5 of A, 5 of B and 1 of C.

i. If Arkon cost Ghc 40 per ton and Zenon Ghc 50 per ton, advise the manufacturer how to minimize cost.

ii. What is the dual of the minimizing LP problem?

Solutions

Expert Solution

i.

Let us assume the following:

Tons of Arkon produced = X1

Tons of Zenon produced = X2

The objective function is cost minimization:

Minimize Z = 40X1 + 50X2

Constraint 1: At least 150 units of A:

3X1 + 5X2 >= 150

Constraint 2: At least 200 units of B:

5X1 + 5X2 >= 200

Cosntraint 3: At least 60 units of C:

3X1 + 1X2 >= 60

Therefore, the linear programming model is formulated as follows:

Minimize Z = 40X1 + 50X2

subject to:

3X1 + 5X2 >= 150

5X1 + 5X2 >= 200

3X1 + 1X2 >= 60

X1, X2 >= 0

Solving the problem using MS Excel Solver:

Therefore, the optimal solution is as follows:

Tons of Arkon produced = X1 = 25

Tons of Zenon produced = X2= 15

Total Cost = ( 40 x 25) + ( 15 x 50) = 1000 + 750 =  Ghc 1750

ii.

Dual of the Minimization problem shall be a maximization problem.

Maximize Zd = 150Y1 + 200Y2 + 60Y3

subject to:

3Y1 + 5Y2 + 3Y3 <= 40

5Y1 + 5Y2 + 1Y3 <= 50

Y1, Y2, Y3 >= 0

keosha answered 7 months ago
Next > < Previous

Related Solutions

A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be...
A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be at least 70% chemical 1, and drug 2 must be at least 60%
chemical 2. Up to 50,000 ounces of drug 1 can be sold at $30 per ounce; up to 60,000 ounces of drug 2 can be sold at $25 per ounce. Up to 45,000 ounces of chemi- cal 1 can be purchased at $15 per ounce, and up to 55,000 ounces of...
A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be...
A chemical manufacturer uses chemicals 1 and 2 to produce two drugs. Drug 1 must be at least 25% chemical 1, and drug 2 must be at least 60% chemical 2. Up to 50,000 ounces of drug 1 can be sold at $27 per ounce; up to 60,000 ounces of drug 2 can be sold at $26 per ounce. Up to 45,000 ounces of chemical 1 can be purchased at $19 per ounce, and up to 55,000 ounces of chemical...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced in the Distilling Department. From the Distilling Department, the materials pass through the Reaction and Filling departments, emerging as finished chemicals. The balance in the account Work in Process—Filling was as follows on January 1: Work in Process—Filling Department (3,400 units, 70% completed): Direct materials (3,400 x $16.80) $57,120 Conversion (3,400 x 70% x $10.90) 25,942 $83,062 The following costs were charged to Work...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced in the Distilling Department. From the Distilling Department, the materials pass through the Reaction and Filling departments, emerging as finished chemicals. The balance in the account Work in Process—Filling was as follows on January 1: Work in Process—Filling Department (4,200 units, 70% completed): Direct materials (4,200 x $16.2) $68,040 Conversion (4,200 x 70% x $10.6) 31,164 $99,204 The following costs were charged to Work...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced in the Distilling Department. From the Distilling Department, the materials pass through the Reaction and Filling departments, emerging as finished chemicals. The balance in the account Work in Process—Filling was as follows on January 1: Work in Process - Filing Department (3,400 units, 60% completed) Direct Materials (3,400 x $9.58) $32,572 Conversion (3,400 x $3.90) $   7,956 TOTAL $40,528 The following costs were charged...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced in the Distilling Department. From the Distilling Department, the materials pass through the Reaction and Filling departments, emerging as finished chemicals. The balance in the account Work in Process—Filling was as follows on January 1: Work in Process—Filling Department (3,400 units, 70% completed): Direct materials (3,400 x $16.80) $57,120 Conversion (3,400 x 70% x $10.90) 25,942 $83,062 The following costs were charged to Work...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced in the Distilling Department. From the Distilling Department, the materials pass through the Reaction and Filling departments, emerging as finished chemicals. The balance in the account Work in Process—Filling was as follows on January 1: Work in Process—Filling Department (4,100 units, 80% completed): Direct materials (4,100 x $17.2) $70,520 Conversion (4,100 x 80% x $11.2) 36,736 $107,256 The following costs were charged to Work...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced in the Distilling Department. From the Distilling Department, the materials pass through the Reaction and Filling departments, emerging as finished chemicals. The balance in the account Work in Process—Filling was as follows on January 1: Work in Process—Filling Department (2,700 units, 80% completed): Direct materials (2,700 x $10.5) $28,350 Conversion (2,700 x 80% x $6.7) 14,472 $42,822 The following costs were charged to Work...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced...
Dover Chemical Company manufactures specialty chemicals by a series of three processes, all materials being introduced in the Distilling Department. From the Distilling Department, the materials pass through the Reaction and Filling departments, emerging as finished chemicals. The balance in the account Work in Process—Filling was as follows on January 1: Work in Process—Filling Department (3,700 units, 60% completed): Direct materials (3,700 x $11.40) $42,180 Conversion (3,700 x 60% x $7.40) 16,428 $58,608 The following costs were charged to Work...
Chemco produces two chemicals A and B. These chemicals are produced via two manufacturing processes. Process...
Chemco produces two chemicals A and B. These chemicals are produced via two manufacturing processes. Process 1 requires 2 hours of labor and 1 lb of raw materials to produce 2 oz of A and 1 oz of B. Process 2 requires 3 hours of labor and 2 lbs of raw material to produce 3 oz of A and 2 oz of B. Sixty hours of labor and 40 lbs of raw material are available. Demand for Chemical A is...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT