he Silver Star Bicycle Company will be manufacturing both men’s and women’s mod-

Question

he Silver Star Bicycle Company will be manufacturing both men’s and women’s mod- els for its Easy-Pedal 10-speed bicycles during the next two months. Management wants to develop a production schedule indicating how many bicycles of each model should be produced in each month. Current demand forecasts call for 150 men’s and 125 women’s models to be shipped during the rst month and 200 men’s and 150 women’s models to be shipped during the second month. Additional data are shown:

ast month the company used a total of 1000 hours of labor. The company’s labor rela- tions policy will not allow the combined total hours of labor (manufacturing plus assem- bly) to increase or decrease by more than 100 hours from month to month. In addition, the company charges monthly inventory at the rate of 2% of the production cost based on the inventory levels at the end of the month. The company would like to have at least 25 units of each model in inventory at the end of the two months.

I have worked through the example and when looking at the solution, I have found that:

My question is: How were those numbers derived? Particularly the positive and the negative signs. I understand its the labor variation for month 2, but I am unsure of how it all came together.

Labor Requirements (hours) Manufacturing Assembly Inventory Production Costs $120 $ 90 Current Model Men's Women's 2.0 1.6 1.5 .30 20 30

Explanation / Answer

Let men = 1, women = 2

Similarly, 1 = month 1, 2 = month 2

x11 = Amount of men's model in month 1 = In x11, first numeric 1 indicate men, second numeric 1 represents month

x21 = Amount of women's model in month 1 = In x21, first numeric 2 represents women and 1 represents month-1

x12 = Amount of men's model in month 2 = In x12, first numeric 1 represents men, and 2 represents month 2

x22 = Amount of women's model in month 2

Labor requirements :

Men's = Manufacturing + Assembly = 2.0 + 1.5 = 3.5

Women's = 1.6 + 1.0 = 2.6

3.5x11 + 2.6x21 is labor smoothing for month 1

3.5x12 + 2.6x22 is labor smoothing for month 2

In order to get actual labor smoothing, we subtract month 2 from month 1. Therefore equation becomes,

3.5x11 + 2.6x21 - 3.5x12 - 2.6x22< 100 (For month 1)

To get month 2, multiply the entire equation with (-) sign, then the equation changes to

-3.5x11 - 2.6x21 + 3.5x12 + 2.6x22 < 100 (for month 2)

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