Bongo has a long term contract (it can be regarded as indefinite) that they must fulfil to provide swimsuits for the local swimming team. The

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Bongo has a long term contract (it can be regarded as indefinite) that they must fulfil to provide swimsuits for the local swimming team. The swimsuits are "one size fits all". The year can be split into two seasons, the summer and the winter seasons. Bongo have to decide how many men's and how many women's swimsuits they need to produce each season indefinitely. The demands for each type of swimsuit for each season are shown in the table below.

Men's swimsuits

1. Winter Demand = 120
2. Summer Demand = 180

Women's swimsuits

1. Winter Demand = 80
2. Summer Demand = 220

Production details for the two products are shown below.

Men's swimsuits

1. MaterialUnits/swimsuit = 2
2. Labour hours/swimsuit = 0.5

Women's swimsuits

1. MaterialUnits/swimsuit = 4
2. Labour hours/swimsuit = 1.25

Material costs $8/unit and labour costs $18/hr. Company policy requires that inventories at the end of each season be at least 10 units for men's swimsuits and 15 units for women's swimsuits. Carrying costs of inventory form one season to the next is 10% of total production cost, i.e. materials plus labour. Union agreements require that the hours worked in any season are not more that 10% higher, or 10% lower that the hours worked in the previous season.

Bongo have the option of hiring a cutting machine that will result in a 20% reduction in material costs if used. The annual hiring cost of the cutting machine is $1,000. The machine could be used to cut, at most, a total of 130 swimsuits a year. Note that the hiring of this machine will not impact inventory holding costs.

Formulate the above problem as an LP to determine the optimal production plan and whether Bongo should rent the cutting machine or not.