Question

The Silver Star Bicycle Company will manufacture both men's and women's models for its Easy-Pedal 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:

			Labor Requirements (hours)
Production Model	Costs		Manufacturing	Assembly	Current Inventory
Men's	$120		2.0	1.5	20
Women's	$90		1.6	1.0	30

Last month, the company used a total of 1,000 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 31 units of each model in inventory at the end of the two months. Hint: Define variables for production and inventory held in each period for each product. Then use a constraint to define the relationship between these: inventory from end of previous period + produced this period - demand this period = inventory at end of this period.

(a)	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 nearest whole number. If your answer is zero, enter “0”.
	Production schedule: The optimal solution is as follows
	Production Schedule Men's Model Women's Model Month 1 _____ _______ Month 2 ____ _______
	Total Cost = $ _____
	Inventory Schedule Men's Women's Month 1 ____ ______ Month 2 ____ _____
	If required, round your answer to two decimal places.
	Labor Levels Previous month _____ hours Month 1 ____hours Month 2 _____hours
(b)	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 nearest whole number.
	Production schedule: The revised optimal solution is as follows
	Production Men's Model Women's Model Month 1 ____ ____ Month 2 ___ _____
	Total Cost = $ _____
	How much will the cost increase?
	$ ______

Answer 1

Sol: Given), the Silver stor cycle company will manufacture both men's and women's model for its easy-pedat bicycles during the next two months. Current demand forecasts call for shipped during the first month men's = 150. kalomen's = 125. Shipped during the second month men's = 200 women's = 150 Inventory from end of previous period + pooduses this period - demand-this pe z of Inventory at end this period. a) 70 establish poodoction schedule: Production Schedule Men's model Women's model 95 Month 193 175 Month 2 162 Total cost =$67, 156 Inventory Schedule: Men's Month 1 Month 2 63 25 women's 0 25 Labour Levels; Previous month - 1000.00 hours

Month 1 992.5 = 923 hours. Momit 2 ; 1022.5 = 1023 hours. by pooduction Schedule : production Men's Women's Month 2 Month 2 201 154 95 175 :: total cost =$67,175 - Increased cost = $ 67,175 - $ 67,156