Operations Research Answers

A school organized a book fair and in this book fair a book seller is selling his books under the following rules:

There are three different packages available.

First package contains 2 Islamic books, 2 Science books and 2 Geography books, second package contains 2 Islamic books, 4 Science books and 1 Geography books and third package contains 3 Islamic books, 4 Science books and 5 Geography books. The book fair has a total of 250 Islamic books, 300 Science books, and 270 Geography books. First package makes a profit of Rs. 120, second package makes Rs.100 and third package makes Rs.270 per pack. 

How many packs should be made to maximize book fair profits?

What will the profit be?

There are two types of fertilizers F1 and F2. F1 consists of 10% nitrogen and 6% phosphoric acid and F2 consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs at least 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If F1 costs Birr 6/kg and F2 costs Birr 5/kg, determine how much of each type of fertilizer should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost? (solve through simplex method)

A can of cat food, guaranteed by the manufacturer to contain at least 10 units of protein, 20 units of mineral matter, and 6 units of fat, consists of a mixture of four different ingredients. Ingredient A contains 10 units of protein, 2 units of mineral matter, and 1 2 unit of fat per 100g. Ingredient B contains 1 unit of protein, 40 units of mineral matter, and 3 units of fat per 100g. Ingredient C contains 1 unit of protein, 1 unit of mineral matter, and 6 units of fat per 100g. Ingredient D contains 5 units of protein, 10 units of mineral matter, and 3 units of fat per 100g. The cost of each ingredient is Birr 3, Birr 2, Birr 1, and Birr 4 per 100g, respectively. How many grams of each should be used to minimize the cost of the cat food, while still meeting the guaranteed composition? (Hint: Solve through simplex model)

Bedele Brewery produces Ale and Beer. Suppose that the productions are limited by scarce resources of Corn, Hops and Barely malt. To make Ale, 5 kg of Corn, 4 Kg of Hops and 35 Kg of Barely malt are required. To make Beer, 15 Kg of Corn, 4 Km of Hops and 20 Kg of Barely malt are required. Suppose that only 480 Kg of Corn, 160 Kg of Hops and 1190 Kg of Barely malt are available. The Brewery plans to enjoy a Profit of Birr 13 for each Kg of Ale and Birr 23 for each Kg of Beer.

Required:

Formulate the linear programming model

How many Ale and Beer should the Brewery Company produce in order to maximize the returns? Using the graphical method. 

What is the total profit? 

Is there any slack?

A furniture manufacturer makes two products - tables and chairs. Processing of these products is done on two types of machines A and B. A chair requires 2 hours on machine type A and 6 hours on machine typeB. A table requires 5 hours on machine type I and no time on Machine type II. There are 16 hours/day available on machine type A and 30 hours/day on machine type B. Profits gained by the manufacturer from a chair & a table are Birr 2 and Birr 10 respectively.What should be the daily production of each of the two products?Use graphical method of LPP to find the solution.

1. Given the following transportation problem:

D1 D2 D3 D4 SS

S1 5 10 7 10 50

S2 9 10 3 3 40

S3 6 4 2 2 60

DD 40 30 10 70

Where D1, D2, D3, and D4 are destinations and the values in the shaded cells are costs;

A. Determine the basic feasible solution through NWCM, LCM and VAM

B. Determine the optimal solution through Stepping Stone and MODI Method

Bedele Brewery produces Ale and Beer. Suppose that the productions are limited by scarce resources of Corn, Hops and Barely malt. To make Ale, 5 kg of Corn, 4 Kg of Hops and 35 Kg of Barely malt are required. To make Beer, 15 Kg of Corn, 4 Km of Hops and 20 Kg of Barely malt are required. Suppose that only 480 Kg of Corn, 160 Kg of Hops and 1190 Kg of Barely malt are available. The Brewery plans to enjoy a Profit of Birr 13 for each Kg of Ale and Birr 23 for each Kg of Beer.

Required:

Formulate the linear programming model

How many Ale and Beer should the Brewery Company produce in order to maximize the returns? Using the graphical method. 

What is the total profit? 

Is there any slack? Identify 

 A firm produces products A, B, and C, each of which passes through assembly and inspection departments. The number of person hours required by a unit of each product in each department is given in the following table.

   Person hours per unit of product

Product A

Product B

Product C

Assembly 

2

4

2

Inspection 

3

2

1

During a given week, the assembly and inspection departments have available at most 1500 and 1200 person-hours, respectively. if the unit profits for products A, B, and C are Birr 50, Birr 40, and Birr 60, respectively, determine the number of units of each product that should be produced in order to maximize the total profit and satisfy the constraints of the problem