Question

Problem 4-19 (Algorithmic)

The Silver Star Bicycle Company will be manufacturing both men’s and women’s models of 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 first month and 200 men’s and 150 women’s models to be shipped during the second month. Additional data are shown:

	Production	Labor Requirements (hours)		Current
Model	Costs	Manufacturing	Assembly	Inventory
Men's	$150	1.9	1.6	30
Women's	$120	1.7	0.9	40

Last month the company used a total of 1000 hours of labor. The company’s labor relations policy will not allow the combined total hours of labor (manufacturing plus assembly) 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 35 units of each model in inventory at the end of the two months.

1. Establish a production schedule that minimizes production and inventory costs and satisfies the labor-smoothing, demand, and inventory requirements. What inventories will be maintained, and what are the monthly labor requirements? If required, round your answers to the nearest whole number.
   
   Production schedule:
   
   The optimal solution is to produce  of the men's model in month 1,  of the men's model in month 2,  units of the women's model in month 1, and  of the women's model in month 2.
   
   Total Cost = $  
   

   Inventory Schedule
   Month 1	Men's	Women's
   Month 2	Men's	Women's

   Labor Levels
   Previous month	hours
   Month 1	hours
   Month 2	hours

2. If the company changed the constraints so that monthly labor increases and decreases could not exceed 50 hours, what would happen to the production schedule? If required, round your answers to the nearest whole number.
   
   Production schedule:
   
   The optimal solution is to produce  of the men's model in month 1,  of the men's model in month 2,  units of the women's model in month 1, and  of the women's model in month 2.
   
   Total Cost = $  
   
   How much will the cost increase?
   
   $  

Answer 1

a.

The model is shown below

The formulas are shown below

The solver parameters are shown below

The result (with all the answers) are shown below

Total cost = 86082

b.

If the labor hour range is changed to 50 from 100, then the result is shown below

Total cost = 86106

Increase in cost = 86106-86082 = 24