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.

Type	Production Hours	Packaging	Shipping	Profit/Tire
SUV tires	1.5	1.5	1	$25
Hatchback tires	2	.75	0.5	$17

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Assuming that the company is interested in maximizing the total profit contribution, answer the following:

a. What are the variables

b. Write all necessary constraints , solve by SOLVER

c. How many tires of each model should Robin manufacture?
d. What is the total profit contribution Robin can earn with the optimal production quantities?

Answer 1

Solution: We will solve the given problem into two parts. In the first part, we will formulate the given problem as a Linear Programming Model, and in the second part, we will solve this LP model.

Part A: Formulate an LP Model:

Decision Variables (Answer a):

Let the decision variables:

S = No. of SUV tires to be manufactured

H = No. of Hatchback tires to be manufactured

Objective Function:

Here, the objective is to maximize the total profit contribution, hence the objective function=

Max Z = 25 S + 17 H

Subject to Constraints (Answer b):

C1 = 1.5 S + 2 H ≤ 500 (Production Hours)

C2 = 1.5 S + 0.75 H ≤ 250 (Packaging Hours)

C3 = 1 S + 0.5 H ≤ 150 (Shipping Hours)

Non-Negativity Condition:

S, H ≥ 0

Part B: Solve the obtained LP (Answer b)

Here, as there is specific information mentioned in the question, we will solve the given LP problem using the MS Excel Solver by following below-mentioned steps:

Step 1: Prepare the following in the excel

(Note: Make Sure to prepare this table in the exact Raws and Columns as mentioned in the below screenshot)

Step 2: Now, type the following formulas in the column of 'Total' as mentioned in the below table. Then, press enter.

Hence, we will get the following table:

Step 3: Now, open Solver ( Data > Analyze > Solver), and fill the exact data in Solver Pop-Up Window as shown in the below screenshot:

Step 4: Once, you press solve button as mentioned in the below step, you will get the following table. Here, the highlighted values are the optimal values for the decision variables:

Hence,

Answer c)

40 SUV and 220 hatchback tires to be manufactured.

Answer d)

Total Profit Contribution = 25 (40) + 17 (220) = 4740 $