Question

Aside from selling yarn skeins, the Yarn Barn also plans to sell men’s and women’s hand-knit

scarves during the next 2 months. The company wants to develop a production schedule indicating

how many scarves of each type should be produced each month. Current demand forecasts show

that 150 men’s and 125 women’s scarves are needed during the first month and 200 men’s and

150 women’s scarves are needed for the second month. Additional data are shown in Figure 2:

			Labour Requirements (hour)
	Production Cost	Knitting	Blocking	Current Inventory
Men’s	$120	2.0	1.5	20
Women’s	$90	1.6	1.0	30

Last month the Yarn Barn used a total of 1000 hours of labor. The company’s labor relation policy

will not allow the combined total hours of labor (knitting and blocking) to increase or decrease by

more than 100 hours from month to month. In addition, the company charges monthly inventory

at a 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 month 2.

8. 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?

a. Provide the linear programming formulation.

b. Solve it using Excel and provided the layout, answer report, and sensitivity report.

9. 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? How much will the

cost increase? What would you recommend?

Answer 1

8)

a) and b)

9)

Increase in cost = 67175-67156 = $19

As it is increasing cost, it is not recommended.