Operations Research Answers

6. 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)

4. Bole cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Birr 5 and that from a shade is Birr 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximize his profit? (Solve by simplex model).

A Kelifa Business Centre plans to sell two models of an item at costs of $350 and $400. The $350 model yields a profit of $85 and the $400 model yields a profit of $90. The total demand per month for the two models will not exceed 150. Find the number of units of each model that should be stocked each month in order to maximize the profit. Assume the merchant can invest no more than $56,000 for inventory of these items.

Formulate Linear Programming problems (LPP)

Find the optimal solution by Graphic method

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?

Q2. 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?

1. A Kelifa Business Centre plans to sell two models of an item at costs of $350 and $400. The $350 model yields a profit of $85 and the $400 model yields a profit of $90. The total demand per month for the two models will not exceed 150. Find the number of units of each model that should be stocked each month in order to maximize the profit. Assume the merchant can invest no more than $56,000 for inventory of these items.

A. Formulate Linear Programming problems (LPP)

B. Find the optimal solution by Graphic method

A farmer can plant upto to 8 acres of land with wheat and barley. He can earn $5000 for every acre he plants with wheat and $3000. His use of necessary pesticides is limited by federal regulations of 10 gallons for his entire 8 acres. Wheat requires 2 gallons of acre for each planted and barley one gallon per acre. What is the maximum profit he can make