Question

In: Operations Management

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 unlimited, but only 20 oz of B can be sold. Chemical A sells for $16/oz, and B sells for $14/oz. Any chemical B that is unsold must be disposed of at a cost of $2/oz. Formulate an LP model to maximize Chemicos revenue and solve.

1. Maximum Revenue

2. Amount of chemical A produced (oz)

3. Amount of chemical B produced and sold (oz)

4. Amunt of chemical B destroyed (oz)

Solutions

Expert Solution

Solution:-

Consider Variable as:-

X1 = Process 1

X2  = Process 2

A = Chemical A produced

B = Chemical B produced

B2  = Chemical unsold

Now,

To maximize chemicos revenue,

Z= ( Cost of A) (Units of process 1) + (cost of B) ( units of process 2)- (cost of B2)(units of B unsold)

Z = 16 (2x1 + 3x2) + 14 (x1 + 2x2 - B2)  - 2B2

Maximize are at the Z value

Z = 16 (2x1 + 3x2) + 14 (x1 + 2x2 - B2)  - 2B2

Let the equation are:-

Constraint 1:- At most, 60 hours of labor are available

[( hour of labor) (Units of chemical produced by process 1) + (hour of labor) (Units of a chemical produced by process 2)]

= 2x1 + 3x2

Constraint 2:- At most, 40 lbs of raw materials are available

[(pounds of raw materials ) (Units of a chemical produced by process 1) + (pounds of materials) (Units of a chemical produced by process 2)]
= x1 + 2x2

Constraint 3:- At most, 20 ounces of chemical B can be sold.

[(ounces of a chemical produced by process 1) + (ounces of a chemical produced by process 2) - (ounces of a chemical unsold)]

x1 + 2x2 - B2

Thus, the formulation of linear programme model is shown as

Maximize Z = 16 (2x1 + 3x2) + 14 (x1 + 2x2 - B2)  - 2B2

Z= 32x1 + 48x2 + 14x1 + 28x2 - 14 B2 - 2B2

Mamimize Z= 46x1 + 76x2 - 16B2

Depending on the constraint

2x1 + 3x2

x1 + 2x2

x1 + 2x2 - B2

Thus all variables x1, x2, B2 are  

keosha answered 1 year ago
Next > < Previous

Related Solutions

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...
Spectre Chemicals produces Canovic in a two-department process. Information on the two departments for March and...
Spectre Chemicals produces Canovic in a two-department process. Information on the two departments for March and April 2016 are as follows: MARCH 2016: Department 1: The Company had beginning inventory of 6,000 units, 40% completed with a cost of $45,000. During the month, the department transferred in 22,000 units of the direct materials with a cost of $10 per unit. Ending inventory was 7,000 units, 30% completed. Direct labor is $310,500 and factory overhead is $103,500. Department 2: The Company...
NO Chart was provided. Spectre Chemicals produces Canovic in a two-department process. Information on the two...
NO Chart was provided. Spectre Chemicals produces Canovic in a two-department process. Information on the two departments for March and April 2016 are as follows: MARCH 2016: Department 1: The Company had beginning inventory of 6,000 units, 40% completed with a cost of $45,000. During the month, the department transferred in 22,000 units of the direct materials with a cost of $10 per unit. Ending inventory was 7,000 units, 30% completed. Direct labor is $310,500 and factory overhead is $103,500....
A manufacturing process has two assembly lines, A and B. Suppose that line A produces 60%...
A manufacturing process has two assembly lines, A and B. Suppose that line A produces 60% of the product. and line B produces the rest. We are told that 5% of the products produced by line A are defective in some way, and 8% of the line B products are defective. it may be helpful to construct a tree diagram with first and second-generation branches to answer the following: C) if the end product is defective, what is the probability...
You are tasked with a process selection project. There are two processes (A and B) that...
You are tasked with a process selection project. There are two processes (A and B) that could potentially work for your application (cutting tubing to a specified length). Sample data is provided by the two companies. Out of the 16 samples from process A, you find an average of 17.92 inches and a standard deviation of 1.98 inches. Thirteen samples were taken from process B improvement and had an average length of 16.58 inches and a standard deviation of 1.30...
QUESTION 3 USE LINGO OR MANUAL LP) Chemco produces three products: A, B, and C. They...
QUESTION 3 USE LINGO OR MANUAL LP) Chemco produces three products: A, B, and C. They can sell up to 30 pounds of each product at the following prices (per pound): product A, $10; product B, $12; product C, $20. Chemco purchases raw material at $5/lb. Each pound of raw material can be used to produce either 1 lb of A or 1 lb of B. For a cost of $3/lb processed, product A can be converted to .6 lb...
A textile company produces two types of materials A and B. The material A is produced...
A textile company produces two types of materials A and B. The material A is produced according to direct orders from furniture manufacturers. The material B is distributed to retail fabric stores. The average production rates for the material A and B are identical at 1,000 meters/hour. By running two shifts the operational capacity of the plant is 80 hours per week. The marketing department reports that the maximum estimated sales for the following week is 70,000 meters of material...
Hormones are chemicals produced by the endocrine system that A) control the formation of urine. B)...
Hormones are chemicals produced by the endocrine system that A) control the formation of urine. B) regulate a variety of body functions, such as metabolism. C) are stimulated by the action of metabolic enzymes. D) function to prevent a variety of diseases, such as diabetes. Which of the following is a nonsteroid hormone? A) ADH B) progesterone C) estrogen D) androgen
Two processes share the variable "I". Process A increments it 10 times and process B decrements...
Two processes share the variable "I". Process A increments it 10 times and process B decrements it 25 times without using critical sections. The initial value of I is 0. The final value of I MUST be Please explain.
A manufacturing company produces water filters for home refrigerators. The process has typically produced some defective...
A manufacturing company produces water filters for home refrigerators. The process has typically produced some defective liters. A random sample of 300 liters yielded 12 defects. Construct and interpret a 90% confidence interval for the true proportion of defective water liters.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT