Operations Research Answers

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.

my mother works as a tutor and a babysitter. she earns 200.00 per hour as a tutor and 100.00 per hour as a babysitter. she renders 12 hours a week. she works to get at least 2,000.00. write the system of inequalities that will represent this situation. find out at least the possible number of hours my mother works as a tutor and a babysitter in a week, by graphing

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 10D AB 10

E B 5

F DE 5

G CF 20 

H DE 10

I GH 15

Use big 𝑀 method solve. 𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑍 = 2𝑦1 + 4𝑦2 𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 2𝑦1 – 3𝑦2 ≥ 2,

−𝑦1 + 𝑦2 ≥ 3; 𝑦1

, 𝑦2 ≥ 0

Use big 𝑀 method to solve Minimize 𝑍 = 6𝑥1 + 3𝑥2 + 4𝑥3 𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜

𝑥1 ≥ 30; 𝑥2 ≥ 50; 𝑥3 ≥ 20; 𝑥1 + 𝑥2 + 𝑥3 = 120

A retired employee wants to invest no more than ₱1,500,000 by buying a stock from a well-known bank and of a university. The stock from the bank offers 7% interest while the stock of a university pays a 5% return. He decided to invest no more than ₱800,000 in the stock from the bank and at least ₱300,000 in the stock of the university. Also, he wants his investment in the stock from the bank to be smaller than his investment in the stock of the university. How much stock should he buy for each investment to maximize his profit? Given that x and y are non-negative, what are some of the constraints? Check whether each constraint is the correct expression for the problem. *

Write the Kuhn-Tucker conditions for the following problems and obtain the optimal solution:

Minimize                    Z= 2x₁+3x₂-x₁²- 2x₂²

Subject to      x₁+3x₂ ≤ 6,

 5x₁+2x₂ ≤ 10,

               x₁, x₂≥ 0