Sleep-EZ Manufacturing Company produces high end home furniture. Sleep-EZ must determine how many units of its Recline-O-Matic chairs to produce each month for the next 3 months. The beginning inventory of finished chairs on August 1 is 100 units. Demand for the chairs is expected to be 1,500 units in August, 2,400 units in September, and 1,800 units in October. Sleep-EZ wants to have 275 completed chairs on hand at the end of October. Production cost is $1,000 per chair in August and is expected to increase by 10% each month. In addition, storage cost from one month to the next is $80 per chair. Due to raw material and labor constraints, the maximum number of chairs Sleep-EZ can produce each month is 2,400, 1,600, and 2,200, respectively. Prepare and solve a linear programming model to determine the production schedule for August, September, and October that will minimize total cost while meeting demand in each month. (Hint: Remember Beg Inv + Prod - Sales = End Inv. You can create and use variables for calculations that are not specifically decision variables. For example, put EndInvAug = 100+ ProdAug - 1500 as a constraint. Then, you can use the variable EndInvAug in your LP.) How many chairs should we produce in August. September, and October? What is the total cost?
Sleep-EZ Manufacturing Company produces high end home furniture. Sleep-EZ must determine how many units of its Recline-O-Matic chairs to produce each month for the next 3 months. The beginning inventory of finished chairs on August 1 is 100 units. Demand for the chairs is expected to be 1,500 units in August, 2,400 units in September, and 1,800 units in October. Sleep-EZ wants to have 275 completed chairs on hand at the end of October. Production cost is $1,000 per chair in August and is expected to increase by 10% each month. In addition, storage cost from one month to the next is $80 per chair. Due to raw material and labor constraints, the maximum number of chairs Sleep-EZ can produce each month is 2,400, 1,600, and 2,200, respectively. Prepare and solve a linear programming model to determine the production schedule for August, September, and October that will minimize total cost while meeting demand in each month. (Hint: Remember Beg Inv + Prod - Sales = End Inv. You can create and use variables for calculations that are not specifically decision variables. For example, put EndInvAug = 100+ ProdAug - 1500 as a constraint. Then, you can use the variable EndInvAug in your LP.) How many chairs should we produce in August. September, and October? What is the total cost?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Sleep-EZ Manufacturing Company produces high end home furniture. Sleep-EZ must determine how
many units of its Recline-O-Matic chairs to produce each month for the next 3 months. The
beginning inventory of finished chairs on August 1 is 100 units. Demand for the chairs is expected to
be 1,500 units in August, 2,400 units in September, and 1,800 units in October. Sleep-EZ wants to
have 275 completed chairs on hand at the end of October. Production cost is $1,000 per chair in
August and is expected to increase by 10% each month. In addition, storage cost from one month to
the next is $80 per chair. Due to raw material and labor constraints, the maximum number of chairs
Sleep-EZ can produce each month is 2,400, 1,600, and 2,200, respectively.
Prepare and solve a linear programming model to determine the production schedule for August,
September, and October that will minimize total cost while meeting demand in each month.
(Hint: Remember Beg Inv + Prod - Sales = End Inv. You can create and use variables for
calculations that are not specifically decision variables. For example, put EndInvAug = 100+
ProdAug - 1500 as a constraint. Then, you can use the variable EndInvAug in your LP.) How
many chairs should we produce in August, September, and October? What is the total cost?
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