In this task, you will solve maximization or minimization problems using the principles of linear programming. You will interpret the feasible region of linear programming and apply the simplex method to solve problems. Make sure to include correct mathematical procedures and provide clear and complete explanations and interpretations. In the case that the result is decimal, you will round it to two decimal places.

1. Use the principles of linear programming to maximize or minimize and interpret the following situation.

Maximize: ?? = 3?? + 4?? Subject to: 2?? + 4??=243?? + 3??=214?? + 2??=20??, ??=0

2. Use the principles of linear programming to maximize or minimize and interpret the following situation.

Minimize: ?? = 3?? + 8?? Subject to: ?? + ??=10?? + 2??=15??=3??, ??=0

3. Sarah makes bracelets and necklaces to sell in a craft store. Each bracelet earns $ 7, takes 1 hour to assemble, and costs $ 2 for materials. Each necklace has a profit of $ 12, takes 2 hours to assemble, and costs $ 3 for materials. Sarah has 48 hours available to put together bracelets and necklaces. If she has $ 78 available to pay for supplies, she uses linear programming principles to determine how many bracelets and necklaces she should make to maximize her earnings.

4. She sue runs a soccer club and must decide how many members to send to soccer camp. She costs $ 75 for each advanced player and $ 50 for each intermediate player. She cannot spend more than $ 13,250. She sue she must send at least 60 more advanced than intermediate players and a minimum of 80 advanced players. She uses the principles of linear programming to find the number of each type of player that she Sue herself can send to camp to maximize the number of players in camp.

5. A company produces two models of calculators at two different plants. In one day, plant A can produce 140 of model 1 and 35 of model 2. In one day, plant B can produce 60 of model 1 and 90 of model 2. Suppose the company needs to produce at least 460 of model 1 and 340 for Model 2, which costs $ 1200 per day to operate Plant A and $ 900 per day for Plant B. Use the principles of linear programming to find the minimum cost.

MG311: Total Quality Management

Calculation (10 marks)

In a workshop, three robots, Q, R and S, are employed to make chairs

Robot Q makes 25% of the chairs

Robot R makes 45% of the chairs

The remaining chairs are made by Robot S

Evidence has shown that 2 percent of the chairs made by robot Q are defective, 3 percent of the chairs made by robot R, and 5 percent of the chairs made by robot S are defective

1. Construct a tree diagram that illustrates all possible outcomes and probabilities (5 marks)

A chair is randomly selected.

1. What is the probability that the chair that robot Q made is defective (1 marks)

(c) What is the probability of findings a broken chair (2 marks)

(d) Given that a chair is defective, what is the probability that it was not made by robot R (2 marks)