Question: The Wearever Carpet Company manufactures two brands of carpet, shag and sculptured, in 100-yard lots....

Question:

The Wearever Carpet Company manufactures two brands of carpet, shag and sculptured, in 100-yard lots. It requires eight hours to produce one lot of shag carpet and six hours to produce one lot of sculptured carpet. The company has the following production goals in prioritized order.

(1) Do not underutilize production capacity, which is 480 hours.

(2) Limit production overtime to 20 hours.

(3) Achieve product demand of forty 100-yard lots for shag and fifty 100-yard lots for sculptured carpet. Meeting demand for shag is more important than meeting demand for sculptured by a ratio of 5 to 2.

(a) Formulate a goal programming model to determine the amount of shag and sculptured carpets to produce to best meet the company’s goals.

(b) Solve this problem (i.e., all the decision variables including the deviational variables should be found) using graphical method. (can use excel solver!!)

Solutions

Expert Solution

(a)

Goal programming model is following:

Decision variables: Let x1, x2 be the number (in 100 yard lots) of shag and scultured carpets to be produced.

di+, di- be the positive and begative deviation variables for i-th goal.

Objective: Min 3*(480/480)*d1- + 2*(5/7)*(480/40)*d2- + 2*(2/7)*(480/50)*d3- + d4+

s.t.

8x1 + 6x2 - d1+ + d1- = 480 (Not underutilize production capacity)

x1 - d2+ + d2- = 40 (satisfy demand for 40 lots of shag carpets)

x2 - d3+ + d3- = 50 (satisfy demand for 50 lots of sculptured carpets)

8x1 + 6x2 - d4+ + d4- = 480+20 (limit overtime production to 20 hours)

x1, x2, di+, di- >= 0

(b)

Solution of the model using LINDO is following (in LINDO model, positive and negative deviation variables are written as dip (for di+) and din (for di-) respectively)

Optimal solution:

x1 = 40

x2 = 30

d1+ = 20

d3- = 20

all other deviation variables = 0

orchestra answered 1 year ago

Next > < Previous

Related Solutions

The Wearever Carpet Company manufactures two brands of carpets-shag and sculptured-in 100 yard lots. It requires...

The Wearever Carpet Company manufactures two brands of carpets-shag and sculptured-in 100 yard lots. It requires 8 hours to produce one lot o shag carpet and 6 hours to produce one lot of sculpture carpet. The company has the following production goals, in prioritized order: 1) Do Not underutilize production capacity, which is 480 hours. 2) Achieve product demand for shag is more important than meeting demand for sculptured, by a ration of 5 to 2. 3) Limit production overtime...

10. The Wearever Carpet Company manufactures two brands of carpet—shag and sculptured—in 10-yard lots. It requires...

10. The Wearever Carpet Company manufactures two brands of carpet—shag and sculptured—in 10-yard lots. It requires 8 hours to produce one lot of shag carpet and 6 hours to produce one lot of sculptured carpet. The company has the following production goals, in prioritized order: (1) Do not underutilize production capacity, which is 480 hours. (2) Achieve product demand of 40 (100-yard) lots for shag and 50 (100-yard) lots for sculptured carpet. Meeting demand for shag is more important than...

The Chris Beehner Company manufactures two lines of designer yard gates, called model A and model...

The Chris Beehner Company manufactures two lines of designer yard gates, called model A and model B. Every gate requires blending a certain amount of steel and zinc; the company has available a total of 25,000 lb of steel and 6,000 lb of zinc. Each model A gate requires a mixture of 125 lb of steel and 20 lb of zinc, and each yields a profit of $90. Each model B gate requires 100 lb of steel and 30 lb...

Carpet Clean manufactures a chemical carpet cleaner. The company was formed during the current year. As...

Carpet Clean manufactures a chemical carpet cleaner. The company was formed during the current year. As a result, there was no beginning inventory. Management is evaluating performance and inventory management issues, and desires to know both net income and ending inventory under generally accepted accounting principles (absorption costing) as well as variable costing methods. Relevant facts are as follows: Selling price per gallon $ 13.00 Variable manufacturing cost per gallon 2.50 Variable SG&A costs per gallon 2.37 Fixed manufacturing costs...

Garden Beauty Inc. is a company that manufactures and sells outdoor yard sculptures. The company president,...

Garden Beauty Inc. is a company that manufactures and sells outdoor yard sculptures. The company president, Karlee Crosby, has expressed a desire to improve the company’s planning for cash needs. She has approached you, a management accounting student, for help in preparing the budget for the upcoming third quarter. She would like to see the sources and uses of cash by month, for the next quarter ending Sept. 30. Your investigations of the company’s records have revealed the following information:...

Buzz Bee Yard Company’ Apiary began operations on January 1, 2020, with the purchase of 100...

Buzz Bee Yard Company’ Apiary began operations on January 1, 2020, with the purchase of 100 bee hives for $500 total. Buzz follows IFRS and its standard on agricultural products. It has completed the first year of operations and has the following information for its bee hives at December 31, 2020: Bee Hives – purchase of hives as per above $ 500 Honey harvested during 2020 (at net realizable value) 1,900 Honey sold during 2020 (at net realizable value)...

Pleasant Hills Properties is developing a golf course subdivision that includes 225 home lots; 100 lots...

Pleasant Hills Properties is developing a golf course subdivision that includes 225 home lots; 100 lots are golf course lots and will sell for $106,000 each; 125 are street frontage lots and will sell for $76,000. The developer acquired the land for $1,910,000 and spent another $1,510,000 on street and utilities improvement. Compute the amount of joint cost to be allocated to the golf course lots using value basis. (Round your intermediate calculation to one decimal place.) Multiple Choice $1,617,660....

a. Port Ormond Carpet Company manufactures carpets. Fiber is placed in process in the Spinning Department,...

a. Port Ormond Carpet Company manufactures carpets. Fiber is placed in process in the Spinning Department, where it is spun into yarn. The output of the Spinning Department is transferred to the Tufting Department, where carpet backing is added at the beginning of the process and the process is completed. On January 1, Port Ormond Carpet Company had the following inventories: Finished Goods $62,000 Work in Process-Spinning Department 35,000 Work in Process-Tufting Department 28,500 Materials 17,000 Departmental accounts are maintained...

FloorMate Carpet Company manufactures carpets. Fiber is placed in process in the Spinning Department, where it...

FloorMate Carpet Company manufactures carpets. Fiber is placed in process in the Spinning Department, where it is spun into yarn. The output of the Spinning Department is transferred to the Tufting Department, where carpet backing is added at the beginning of the process and the process is completed. On October 1, FloorMate Carpet Company had the following inventories: Finished Goods $7,200 Work in Process-Spinning Department 1,000 Work in Process-Tufting Department 2,400 Materials 4,300 Departmental accounts are maintained for factory overhead,...

FloorMate Carpet Company manufactures carpets. Fiber is placed in process in the Spinning Department, where it...

FloorMate Carpet Company manufactures carpets. Fiber is placed in process in the Spinning Department, where it is spun into yarn. The output of the Spinning Department is transferred to the Tufting Department, where carpet backing is added at the beginning of the process and the process is completed. On October 1, FloorMate Carpet Company had the following inventories: Finished Goods $8,400 Work in Process-Spinning Department 1,600 Work in Process-Tufting Department 2,100 Materials 4,500 Departmental accounts are maintained for factory overhead,...

Subjects