# Answered Essay: Greenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of 4,100 bookshelf speakers and 4,900 floor speakers over the next two months, with the following delivery schedule:

Problem 4-21 (Algorithmic)

Greenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of 4,100 bookshelf speakers and 4,900 floor speakers over the next two months, with the following delivery schedule:

 Model Month 1 Month 2 Bookshelf 2,500 1,600 Floor 1,900 3,000

Greenville estimates that the production time for each bookshelf model is 0.8 hour and the production time for each floor model is 1 hour. The raw material costs are \$14 for each bookshelf model and \$16 for each floor model. Labor costs are \$26 per hour using regular production time and \$37 using overtime. Greenville has up to 2,800 hours of regular production time available each month and up to 1,400 additional hours of overtime available each month. If production for either cabinet exceeds demand in month 1, the cabinets can be stored at a cost of \$9 per cabinet. For each product, determine the number of units that should be manufactured each month on regular time and on overtime to minimize total production and storage costs. If required, round your answers to the nearest whole number.

 Regular Time Manufacture Model Month 1 Month 2 Bookshelf Floor
 Overtime Manufacture Model Month 1 Month 2 Bookshelf Floor

Decision variables for Regular

Bookshelf for month1 =B1R

Bookshelf for month2=B2R

Floor for month1=F1R

Floor for month2=F2R

Decision variable for overtime

Bookshelf for month1 =B1O

Bookshelf for month2=B2O

Floor for month1=F1O

Floor for month2=F2O

Labor cost per unit

Bookshelf for regular =0.8*26 = \$20.8

Bookshelf for overtime =0.8*37 = \$29.6

Floor for regular =1*26 =\$26

Floor for overtime = 1*37 =\$37

IB = month 1 ending inventory for bookself units

IF= month 1 ending inventory for floor model

Objective function:

Min 20.8 B1R + 20.8 B2R + 26 F1R + 26 F2R + 29.6 B1O + 29.6 B2O + 37 F1O + 37 F2O + 14 B1R + 14 B2R + 16 F1R + 16 F2R + 14 B1O + 14 B2O + 16 F1O + 16 F2O + 9 IB + 9 IF

Min. 34.8B1R +34.8B2R+42F1R+42F2R+43.6B1O+43.6B2O+53F1O+53F2O +9IB+9IF

Such that

.8 B1R + 1 F1R < 2800 Regular time: month 1

.8 B2R + 1 F2R < 2800 Regular time: month 2

.8B1O + 1 F1O < 1400 Overtime: month 1

.8B2O + 1 F2O < 1400 Overtime: month 2

B1R + B1O – IB = 2500 Bookshelf: month 1

IB + B2R + B2O = 1600 Bookshelf: month 2

F1R + F1O – IF = 1900 Floor: month 1

IF + F2R + F2O = 3000 Floor: month 2

Using Excel solver

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