Question & Answer: A manufacturer of tires produces two kinds of tires. The premium tire, The Last-Forever, is a…..

A manufacturer of tires produces two kinds of tires. The premium tire, The Last-Forever, is a
steel-belted, puncture-resistant, long-wear tire that holds all records for quality within the industry.
The other tire, Lane-Handler, is a simple low cost 40,000 mile warranty unbranded tire. The
Last-Forever contributes \$50 per tire to the bottom line for the company, while the Lane-Handler
contributes only \$10 to the bottom line. Both tires are manufactured at the same factory and require
the same machines to be produced. Machine A and machine B are both used in the two-step process
used to make the tires. The time consumed in hours on each machine to fabricate a tire are given
below.

Machine A
Lane-Handler – 1
Last-Forever – 4
Total Hours Available – 120

Machine B
Lane -Handler – 2
Last-Forever – 2
Total Hours Available – 100

Twenty Lane-Handlers have been promised to a valued dealer and 4 Last-Forevers have been
promised the owner’s son.
(a) Find the product mix that maximizes profit.
(b) What is the OV? (optimal solution or objective function value)
(c) If machine B hours could be increased to 120, then what would be the change in the OV?
(d) What would be the impact if a maintenance problem reduced available machine A hours
to 100?

a) max z = 50*4 X (last forevers) + 10*20 Y (lane handlers)

eq.1- $\fn_cm 4X + Y \leq 120$

eq.2 $\fn_cm 2X + 2Y \leq 100$

X, Y $\fn_cm \geq$ 0

b) Objective function value is \$10000 is the max profit.

C) if machine B hours Incresed to be 120, then the Max profit will be \$12000.

d) if machine A hours reduced to 100 hours then the profit will be remain same to \$10000.