In the problem on excel : 1.What are the decision variables 2.What is the objective functions 3. What are the constraints and explain A used t company, owned by Musa in Ottawa sells 7 different brands covering 3 different products. These are 4 Brands of Cars: Toyota, Honda, Chevrolet and BMW; 2 brands of Motorcycles: Suzuki and Yamaha, and 1 brand of Sailboats: Amel. Musa knows that his sales floor which he will display his products is 70,000 square feet, and that a Car takes 60 square feet of space, a motorcycle takes 20 square feet of space, and a sailboat takes 800 square feet of space. The profit that can be made for selling each of 7 different items is listed below: ITem Profit per unit Car - Toyota $2800 Car - Honda $3900 Car - Chevrolet $2,100 Car - BMW $5000 Motorcycle - Suzuki $1,000 Motorcycle - Yamaha $2,250 Sailboat - Amel $9,500 The transportation company is trying to determine how many of each item to order to maximize profit, given the following restrictions: 1. Musa must order exactly $800 total items. 2. The number of Cars to order must be between 400 and 750 3. Musa would like to have between 4 and 6 times as many Honda Cars as Yamaha Motorcycles. 4. The number of Honda Cars available, must be exactly 65 more then the number of Chevrolet Cars available. 5. Since Ottawa is a wealthy community, Musa decides that he must have at-least as many Amel Sailboats compared to the total number of Motorcycles. 6. There must be at-least 5 each of the two least profitable units. 7. Together, the total number of Amel Sailboats and Toyota Cars must equal the total number of Yamaha Motorcycles and Chevrolet Cars combined. How many of each Brand of each product should Musa bring into his transportation company to maximize profit?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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In the problem on excel : 1.What are the decision variables 2.What is the objective functions 3. What are the constraints and explain A used t company, owned by Musa in Ottawa sells 7 different brands covering 3 different products. These are 4 Brands of Cars: Toyota, Honda, Chevrolet and BMW; 2 brands of Motorcycles: Suzuki and Yamaha, and 1 brand of Sailboats: Amel. Musa knows that his sales floor which he will display his products is 70,000 square feet, and that a Car takes 60 square feet of space, a motorcycle takes 20 square feet of space, and a sailboat takes 800 square feet of space. The profit that can be made for selling each of 7 different items is listed below: ITem Profit per unit Car - Toyota $2800 Car - Honda $3900 Car - Chevrolet $2,100 Car - BMW $5000 Motorcycle - Suzuki $1,000 Motorcycle - Yamaha $2,250 Sailboat - Amel $9,500 The transportation company is trying to determine how many of each item to order to maximize profit, given the following restrictions: 1. Musa must order exactly $800 total items. 2. The number of Cars to order must be between 400 and 750 3. Musa would like to have between 4 and 6 times as many Honda Cars as Yamaha Motorcycles. 4. The number of Honda Cars available, must be exactly 65 more then the number of Chevrolet Cars available. 5. Since Ottawa is a wealthy community, Musa decides that he must have at-least as many Amel Sailboats compared to the total number of Motorcycles. 6. There must be at-least 5 each of the two least profitable units. 7. Together, the total number of Amel Sailboats and Toyota Cars must equal the total number of Yamaha Motorcycles and Chevrolet Cars combined. How many of each Brand of each product should Musa bring into his transportation company to maximize profit?

Expert Solution

Step 1

Linear Programming is a statistical and mathematical technique that helps an organization to know how a quantity is to be produced or ordered or purchased so that total cost can be minimized or profit can be maximized. Organizations use this model as it helps in determining what resources are not contributing towards profit and how to manage the current level of active resources. It is still quite popularly used in companies when they are not able to reach a particular decision.

Let all four brands of the car be T, H, C, and B. 2 brands of motorcycle S and Y. One brand of the sailboat is considered A.

Profit to be maximized:

$Z = 2800 T + 3900 H + 2100 C + 5000 B + 1000 S + 2250 Y + 9500 A$ (Objective Function)