Operations Research Answers

1)   3F manufacturer produces two products: Beds and Chairs. Each unit of Bed requires 3 hrs in molding unit, 4hrs in painting unit, and 1 hr in finishing. On the other hand, each unit of Chair requires 3 hrs in molding unit, 2 hrs in the paint shop and 2 hours in finishing. Each week, there are 210 hrs available in molding, 200hrs in painting, and 120 hrs in finishing unit. The demand for Beds cannot exceed 40 units per week. Each unit of Bed contributes Birr 20 to profit, while each unit of chair contributes Birr 30. Determine the number of units of each product per week to maximize the profit?

A factory produces three types of fertilizer: X1, X2 and X3. The profits realized from a kilo of each typeare P25, P15 and P35, respectively. The raw materials from which fertilizers are made are nitrogen, sulfurand potassium which are used in the following quantities:NitrogenSulfurPotassiumX13 kilos4 kilos8 kilosX23 kilos4 kilos1 kiloX32 kilos5 kilos3 kilosThe available stocks include 1,500 kilos of nitrogen, 1000 kilos of sulfur and 1200 kilos of potassium. Theobjective is to maximize profit. Find the amounts of X1, X2 and X3 to be manufactured

Steel can be produced using three different methods: The following table lists the average cost per ton of steel for each method.

Type of Cost Basic Continuous Electric

Process Casting Furnace

Materials 150 140 120

Labor 80 75 70

Capital 100 100 60

Energy 20 15 50

Other 45 40 25

a. Production of steel by electric furnace is a relatively new development (beginning in late 1970s) and accounts for a growing fraction of total steel sold. What is your prediction about the future production share of this method?

b. If there were a new energy crisis how would this affect steel makers choices of production methods?

c. Suppose the price of steel scrap is expected to fall significantly over the next five years. What effect would this have on the choice of production method?

How to draw a network diagram in mathematical foundations of computer science

How steps to draw a network diagram.

What and Define is network diagram

A-ONE publisher and sells books. The management is in the process of printing a new book to be marked. 

The book may be bound by either cloth or paperback. Each cloth bound book sold out bring a profit of Rs 

60 and each paper bound book contributes Rs 35. It takes 10 minutes to bind a cloth cover and 8 minutes 

to bind a paperback. The total available time for binding is 20 hours. After considerable market surrey, it is 

predicated that the cloth cover sales will not exceed 800 copies and the paperback sales will be no more 

than 1200 copies. Formulate as an LP model with an appropriate objective function and constraints.

A small business enterprise makes dresses and trousers. To make a dress

requires 1

2

hour of cutting and 20 minutes of stitching. To make a trouser

requires 15 minutes of cutting and 1

2

hours of stitching. The profit on a dress is

P40 and on a pair of trousers is P50. The business operates for a maximum of

8 hours per day. Determine how many dresses and trousers should be made to

maximize profit and what the maximum profit is.

Consider a project consisting of nine jobs (A, B, C,….,I) with the following precedence

relations and time estimates.

Job Predecessor Time (Days)

A -- 15

B -- 10

C A,B 10

D AB 10

E B 5

F DE 5

G CF 20

H DE 10

I GH 15

a. Draw the project network for this problem designating the jobs by arcs and event by nodes. b.

Determine the earliest completion time of the project, and identify the critical path.

c. Determine a project schedule listing the earliest and latest starting times of each job. Also identify

the critical job.