Greenville Cabinets received a contract to produce speaker cabinets for a major
ID: 444125 • Letter: G
Question
Greenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of 3300 bookshelf speakers and 4100 oor speakers over the next two months, with the following delivery schedule:
Model
Month 1
Month 2
Bookshelf
2100
1200
Floor
1500
2600
Greenville estimates that the production time for each bookshelf model is 0.7 hour and the production time for each oor model is 1 hour. The raw material costs are $10 for each bookshelf model and $12 for each oor model. Labor costs are $22 per hour using regular production time and $33 using overtime. Greenville has up to 2400 hours of regular production time available each month and up to 1000 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.
Model
Month 1
Month 2
Bookshelf
2100
1200
Floor
1500
2600
Explanation / Answer
Decision variables: Regular
Model Month 1 Month 2
Bookshelf B1R B2R
Floor F1R F2R
Decision variables: Overtime
Model Month1 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
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