Problem 1 : X Corp manufactures benches and tables. They have two main resources: labor force and a supply of redwood used in the furniture. During the next production cycle, 1200 hour of labor are required under a union agreement. X Corp also has a stock of 3,500 feet of good quality redwood. Each bench requires 4 labor hours and 10 feet of redwood; each table requires 6 labor hours and 35 feet of redwood. Complete benches will yield a profit of $9.00 each, the table, $20.00 profit each. How many benches and tables should X Corp produce to yield the largest possible profit? Use the graphical LP approach.

Problem 2 : The nuclear plant currently has 350 fully trained workers. They need to know how many worker are need to be trained for the remainder if the year.

The law permits no more than 130 hours per month per employee. Slightly over 1 hour per day is used for check-in and check-out, record-keeping and for daily radiation scans. Policy is that no layoffs are permitted in those months when the plant is over staffed. So, if more workers are trained than are needed in any month, they are still paid but not required to work the 130 hours.

Trainees must be hired 1 month before they are needed. Each trainee teams up with a skilled worker and requires 90 hours of that employee’s time. This mean the skilled worker is not available for those 90 hours during this month.

There is a turnover rate of trained workers of 5% per month. (5% of the trained employees at the start of the month resign by the end of the month) A trained worker earns an average of $2,000 per month, regardless of the number of hours worked. Trainees are paid $900 during their one month of instruction.

1. Formulate this staffing problem using LP.
2. Solve the problem. How many trainees must begin each month?

Problem 3 : Consider the following LP problem:

& \max \text{ }0.8{{x}_{1}}+0.4{{x}_{2}}+1.2{{x}_{3}}-0.1{{x}_{4}} \\

& \text{s}\text{.t}\text{. }{{x}_{1}}+2{{x}_{2}}+{{x}_{3}}+5{{x}_{4}}\le 150 \\

& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{2}}-4{{x}_{3}}+8{{x}_{4}}=70 \\

& \,\,\,\,\,\,\,\,\,\,\,\,6{{x}_{1}}+7{{x}_{2}}+2{{x}_{3}}-{{x}_{4}}\ge 120 \\

& \,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{1}},{{x}_{2}},{{x}_{3}},{{x}_{4}}\ge 0 \\

\end{aligned}\]

1. Convert the constraints to equalities by adding the appropriate slack, surplus or artificial variable. Also, add the new variables into the problem’s objective function.
2. Set up the complete initial simplex tableau for this problem.
3. Give the values for all variables in this initial solution.

Price: $17.09

Solution: The downloadable solution consists of 8 pages, 909 words and 1 charts.
Deliverable: Word Document