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?