Question

QUESTION 80 Use the table below to answer the following question(s). Remington Textiles has a mill that produces three types of fabrics on a make-to-order basis. The mill operates on a 24/7 basis. The key decision facing the plant manager is about the type of loom needed to process each fabric during the coming 12 weeks to meet demands for the three fabrics and not exceed the capacity of the looms in the mill. Two types of looms are used: Jaquard and Northrop. Jaquard looms can be used to make all fabrics and are the only looms that can weave certain fabrics, such as plaids. Demands, variable costs for each fabric, and production rates on the looms are given in the table below. The mill has 10 Northrop looms and 2 Jaquard looms. Any fabrics that cannot be woven in the mill because of limited capacity will be purchased from an external supplier, finished at the mill, and sold at the selling price. In addition to determining which looms to use to process the fabrics, the manager also needs to determine which fabrics to buy externally Remington extiles Data Jaquard Northrop pacity Mill Cost Demand Capacity (yards) ards/hour)(yards/hour) (S/yard) 50,000 5.6 62,000 5.2 35,000 4.8 utsourcing Cost (S/yard) 0.81 0.85 0.84 Fabric 0.53 0.6 0.71 Answer the following questions using a linear optimization model. According to the model, what is the total amount of Fabric 1 to be produced on Jaquard? O 50,000 22,579.2 27,420.8

Answer 1

Let,

xi = yards of fabric i to produce on Jaquard loom

yi = yards of fabric i to produce on Northop loom

pi = yards of fabric i to be purchased from external supplier

Objective is to minimize cost = Min 0.53x1 + 0.6x2 + 0.71x3 + 0.6y2 + 0.71y3 + 0.81p1 + 0.85p2 + 0.84p3

Subject to following constraints,

1. Demand Constraints

x1+p1 = 50000 (Demand should be exactly matched)

x2+y2+p2 = 62000 (Demand should be exactly matched)

x3+y3+p3 = 35000 (Demand should be exactly matched)

2. Capacity constraints

available hours for Jaquard = 24 hours/day * 7 days/week* 12 weeks*2 looms = 4032

capacity of Jaquard for fabric 1 = 5.6 yards/hour we can say per hour capacity = 1/5.6 per hour

1/5.6 x1 + 1/5.2 x2 + 1/4.8 x3 <= 4032
or,0.17857x1 + 0.19230X2 + 0.20833X3 <= 4032 -----(1)

available hours for Northorp = 24 hours/day * 7 days/week* 12 weeks*10 looms = 20160

1/4.8Y2 + 1/4.5Y3 <= 20160

OR, 0.20833Y2 + 0.22222Y3 <= 20160

xi,yi,pi >= 0 (non-negativity constraints)

Solving in excel solver we get,

x1 = total amount of fabric 1 to be produced on Jaquard = 22579.38

Correct answer is 22579.2 (Ans)

賕 x3y2 ysp2p3 0 62000 32596.26 27420.62 0 2403.744 Objective function 96540.26 5 Demand-fabric1 50000 62000 135000 50000 62000 35000 4032 20160 7 Demand-fabric3 8|capacity of Jaquard 9 capacity of Northonp 100 .17857 0.1923 0.20833 4032 <= 20160 0.20833 0.22222 10