A local computer supply company produces a large variety of products but it\'s t

Question

A local computer supply company produces a large variety of products but it's two top selling products are it's USB mouse and USB flash drive. There are three production departments: Fabrication, Assembly, & Inspection and Packaging. The table below shows the profit per unit of each product along with its associated production requirements: Inspection & Profit per Assembly ProductsUnit(in mins) (in mins) mins) USB Mouse $4 10 3 USB Flash Drive $1 2 2 2 Total time Total time Total time available available available 10 30 24 Using the information about, what is the maximum proft the company should expect if it produces the optimal amount of each USB Mouse and USB Flash Drive?

Explanation / Answer

Let the number of units of mouse be x

Let the number of units of flash drive be y

Profit Function, Z = 4x + y

Constraints:

10x + 2y <= 30 (fabrication)

3x + 2y <= 24 (assembly)

2x + 2y <= 10 (packaging)

solving these constraints with the Z(profit function) we get

The maxima occurs when x=2.5 and y=2.5, which is not possible, since values must be an integer

Hence we can make 2 mouses and 3 flash drives, in order to meet all possible requirements and making it integer

Hence the final optimal value Z = 4(2) + 1(3) = 11 $

Other possible integer solution is

Hence we can make 3 mouses and 0 flash drives, in order to meet all possible requirements and making it integer

Hence the final optimal value Z = 4(3) + 1(0) = 12 $

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