Question

Robin Tires, Inc. makes two types of tires, one for SUVs and the other for Hatchbacks. The firm has the following limits -500 hours for production, 250 hours for packaging, and 150 hours for shipping. The times required per tire type is given in the following table: Production Hours Shipping Profit/Tie Production Packaging Type $22 S12 1.5 UV tires Hatchbacks tires 0.5 1.5 Assuming that the company is interested in maximizing the total profit contribution, formulate this linear optimization problem. Let s- number of SUV tires manufactured and H - number of Hatchbacks tires manufactured Max subject to S1 Hs 22 (production constraint) S5Hs 12 (packaging constraint) +0.5 Hs(shipping constraint) S H z 0 (non-negativity constraints)

please explain steps i am confused

Answer 1

The decision variables are

S and H for number of SUV tires and number of Hatchback tires

The unit profit is $22 for S and $12 for H so we need to maximize the profit

The objective function would be

$22S+$12H

Constraints

Production hour constraints

The unit time required for S and H is 2 and 1.5 hours respectively and the total time available is 500 hours

So the constraint would be

2S+1.5H<= 500

Similarly, for packaging, the constraint would be

1.5S+1H<=250

For Shipping

1S+0.5H<=150

S,H>= 0 (non negativity constraint)

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