Problem 4-21 Sreenville Cabinets received a contract to produce speaker cabinets

Question

Problem 4-21 Sreenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of 3,300 bookshelf speakers and 4,100 floor speakers over the next two months, with the following delivery schedule: Model Bookshelf Floor Month 1 2100 1500 Month 2 1200 2600 Greenville estimates that the production time for each bookshelf model is 0.7 hour and the production time for each floor model is 1 hour. The raw material costs are $10 for each bookshelf model and $12 for each floor model. Labor costs are $22 per hour using regular production time and $33 using overtime. Greenville has up to 2,400 hours of regular production time available each month and up to 1,000 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 $5 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. If an amount is zero, enter "o0". Use a software package LINGO or Excel Solver Regular Time Manufacture Month 2 Month 1 1,900 1,900 Model Floor Overtime Manufacture Month 1 Month 2 Model Bookshelf Floor Previous Next Check My Work Email Instructor Save and Exit Submit Assignment for Grading All work saved. 100% 8:51 AM

Explanation / Answer

Decision variables: Regular

Model             Month1       Month 2

Bookshelf      B1R              B2R

Floor             F1R                F2R

Decision variables: Overtime

Model          Month 1          Month 2

Bookshelf      B1O               B2O

Floor             F1O                 F2O

Labor costs per unit

Model            Regular                   Overtime

Bookshelf     .7 (22) = 15.40        .7 (33) = 23.10

Floor              1 (22) = 22             1 (33) = 33

IB = Month 1 ending inventory for bookshelf units

IF = Month 1 ending inventory for floor model

Objective function

Min 15.40 B1R + 15.40 B2R + 22 F1R + 22 F2R + 23.10 B1O + 23.10 B2O + 33 F1O + 33 F2O + 10 B1R + 10 B2R + 12 F1R + 12 F2R + 10 B1O + 10 B2O + 12 F1O + 12 F2O + 5 IB + 5 IF

or

Min 25.40 B1R + 25.40 B2R + 34 F1R + 34 F2R + 33.10 B1O + 33.10 B2O + 45 F1O + 45 F2O + 5 IB + 5 IF

s.t.

.7 B1R + 1 F1R < 2400 Regular time: month 1

.7 B2R + 1 F2R < 2400 Regular time: month 2

.7B1O + 1 F1O < 1000 Overtime: month 1

.7B2O + 1 F2O < 1000 Overtime: month 2

B1R + B1O - IB = 2100 Bookshelf: month 1

IB + B2R + B2O = 1200 Bookshelf: month 2

F1R + F1O - IF = 1500 Floor: month 1

IF + F2R + F2O = 2600 Floor: month 2

OPTIMAL SOLUTION

Optimal Objective Value 241129.99940, which are the minimum costs.

Variable Value

B1R      1228.57143

B1O        871.42855

B2R         0.00000

B2O         1200.00000

IB             0.00000

F1R        1540.00000

F1O      0.00000

F2R        2400.00000

F2O        160.00000

IF            40.00000

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