Question

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. Let Ji represent the number of yards of fabric i to be produced on Jaquard looms, and Ni be the number of yards of fabric i to be produced on Northrop looms.

Fabric	Demand (yards)	Jaquard Capacity (hours/yard)	Northrop Capacity (hours/yard)	Mill Cost ($/yard)	Outsourcing Cost ($/hour)
1	50,000	0.2	NA	0.53	0.81
2	62,000	0.2	0.2	0.6	0.85
3	35,000	0.25	0.25	0.71	0.84

What is the correct constraint for expressing the capacity of Jaquard looms?

5J1 + 5J2 + 4J3 ≤ 20160

5J1 + 5J2 + 5J3 ≤ 4032

0.2J1 + 0.2J2 + 0.25J3 ≤ 4032

0.2J1 + 0.2J2 + 0.25J3 ≤ 20160

Answer 1

The correct answer is :0.2*J1+0.2*J2+0.25*J3<= 4032

Given : The mill operates 24*7

For 12 weeks ,total number of hours available in Jaquard loom=24*7*12=2016

For 2 Jaquard looms,

Total number of hours available =2016*2=4032

The capacity constraint is ,

0.2*J1+0.2*J2+0.25*J3<= total number of hours available

0.2*J1+0.2*J2+0.25*J3<= 4032