**Assignment Solutions on Management Quantitative Analysis for Decision Making**

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**Assignment Details:-**

**Words:**3000**Document Type:**Assignment Help (any type)**Subject:**Management**Citation/Referencing Style:**Any

**Group Assignment I **

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

a. Formulate Linear Programming problems (LPP)

b. Find the optimal solution by Graphic method

2. 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 type B. 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.

a. What should be the daily production of each of the two products?

b. Use graphical method of LPP to find the solution.

3. Tigist wishes to mix two types of food C and D in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin C and 11 units of vitamin D. Food C costs $ 60/kg and Food D costs $80/kg. Food C contains 3 units/kg of Vitamin A and 5 units / kg of Vitamin B while food D contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture by graphic model.

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).

5. A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Birr 25000 and Birr 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Birr 70 lakhs and if his profit on the desktop model is Birr 4500 and on portable model is Birr 5000. (Find optimal Solution by simplex Model)

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)

7. A manufacturer has three machines I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for at least 5 hours a day. She produces only two items M and N each requiring the use of all the three machines. The number of hours required for producing 1unit of each of M & N on the three machines are given in following table

Items | Numbers of hours required on machines | ||

I | II | III | |

M | 1 | 2 | 1 |

N | 2 | 1 | 1.25 |

She makes a profit of Birr 600 and Birr 400 on items M and N respectively. How many

of each item should she produce so as to maximize her profit assuming that she can sell

all the items that she produced? What will be the maximum profit? (Solve through simplex method)

8. A company manufactures two products X and Y. Each product has to be processed in three departments: welding, assembly and painting. Each unit of X spends 2 hours in the welding department, 3 hours in assembly and 1 hour in painting. The corresponding times for a unit of Y are 3, 2 and 1 respectively. The man-hours available in a month are 1500 for the welding department, 1500 in assembly and 550 in painting. The contribution to profits are $100 for product X and $120 for product Y.

a. Formulate the appropriate linear programming problem

b. Solve it graphically to obtain the optimal solution for the maximum contribution

9. A company manufactures two products P1 and P2. Profit per unit for P1 is $200 and for P2 is $300. Three raw materials M1, M2 and M3 are required. One unit of P1 needs 5 units of M1 and 10 units of M2. One unit of P2 needs 18 units of M2 and 10 units of M3. Availability is 50 units of M1, 90 units of M2 and 50 units of M3.

a. Formulate as LPP

b. Find the optimal by using simplex method

10. 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)

11. Wodera cooperative society of farmers has 50 hectare of land to grow two crops X and Y. The profit from crops X and Y per hectare are estimated as Birr 10,500 and Birr 9,000 respectively. To control weeds, a liquid herbicide has to be used for crops X and Y at rates of 20 liters and 10 liters per hectare. Further, no more than 800 liters of herbicide should be used in order to protect fish and wild life using a pond which collects drainage from this land. How much land should be allocated to each crop so as to maximize the total profit of the society? (Solve By graphic method).

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