Greenville Cabinets received a contract to produce speaker cabinets for a major
ID: 407895 • 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 floor speakers over the next two months, with the following delivery schedule.
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 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, we would like to determine the number of units that should be manufactured each month on regular time and on overtime to minimize total production and storage costs.
a) Formulate an LP model for this problem.
Explanation / Answer
Answer is:
Bookshelf = X
Floor = Y
Overtime labour = O
Regular Time Labour:
Model Month 1 Month 2
Bookshelf B1X B2X
Floor F1Y F2Y
Decision variables: Overtime labor
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
Inventory Bookshelf = Month 1 ending inventory for bookshelf units
Inventory for Floor = Month 1 ending inventory for floor model
Min 15.40 B1X + 15.40 B2X + 22 F1Y + 22 F2Y + 23.10 B1O + 23.10 B2O + 33 F1O + 33 F2O + 10 B1X + 10 B2X + 12 F1Y + 12 F2Y + 10 B1O + 10 B2O + 12 F1O + 12 F2O + 5 IB + 5 IF
.7 B1X + 1 F1Y < 2400 Regular time: month 1
.7 B2X + 1 F2Y < 2400 Regular time: month 2
.7B1O + 1 F1O < 1000 Overtime: month 1
.7B2O + 1 F2O < 1000 Overtime: month 2
B1X + B1O - IB = 2100 Bookshelf: month 1
IB + B2X + B2O = 1200 Bookshelf: month 2
F1Y + F1O - IF = 1500 Floor: month 1
IF + F2Y + F2O = 2600 Floor: month 2
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