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.

Remington Textiles
Data
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	025	0.25	0.71	0.84

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

Group of answer choices

0.2N2 + 0.25N3 ≤ 4032

0.2N2 + 0.25N3 ≤ 20160

5N1 + 5N2 + 5N3 ≤ 4032

5N1 + 5N2 + 4N3 ≤ 20160

Answer 1

Ni is the number of yards of fabric i to be produced on Northrop looms.

For 12 weeks, number of hours, a Northrop loom will be running = 12 * 7 * 24 = 2016

Total capacity of 10 Northrop looms = 10 * 2016 = 20160

Total capacity to meet the demand of each fabric = 0.2N2 + 0.25N3

The constraint for expressing the capacity of Northrop looms is that the total capacity to meet the demand of each fabric should be at most 20160 hours which is,

0.2N2 + 0.25N3 ≤ 20160