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198 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

forecasts for March, April and May are for 12 000 units, 8 000 units and 15 000 units,
respectively. In addition, Filtron has the capacity to store up to 3000 filtration containers
at the end of any month. Management would like to determine the number of units to be
produced in March, April and May that will minimize the total cost of the monthly
production increases and decreases.
16 Jansson Cabinets received a contract to produce loud speaker cabinets for a major
hi-fi 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.

Model Month 1 Month 2

Bookshelf 2 100 1 200
Floor 1 500 2 600

Jansson estimates that the production time for each bookshelf model is 0.7 hours
and the production time for each floor model is one hour. The raw material costs are
E10 for each bookshelf model and E12 for each floor model. Labour costs are E22 per
hour using regular production time and E33 using overtime. Jansson 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 E5 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.
17 EZ-Windows manufactures replacement windows for the home renovation business. In
January, the company produced 15 000 windows and ended the month with 9000
windows in inventory. EZ-Windows management team would like to develop a
production schedule for the next three months. A smooth production schedule is
obviously desirable because it maintains the current workforce and provides a
similar month-to-month operation. However, given the sales forecasts, the
production capacities and the storage capabilities as shown, the management team
does not think a smooth production schedule with the same production quantity each
month possible.

February March April
Sales forecast 15 000 16 500 20 000
Production capacity 14 000 14 000 18 000
Storage capacity 6 000 6 000 6 000

The company’s cost accounting department estimates that increasing production by one
window from one month to the next will increase total costs by E1.00 for each unit increase
in the production level. In addition, decreasing production by one unit from one month to
the next will increase total costs by E0.65 for each unit decrease in the production level.
Ignoring production and inventory carrying costs, formulate and solve a linear
programming model that will minimize the cost of changing production levels while still
satisfying the monthly sales forecasts.

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