Operations Research Answers

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