Please See attached document

1) A freelance writer must choose how to spend her time working on several different types of projects.

               Newspaper stories take 3 hours to write and pay a flat rate of $45 per story. Magazine articles take much longer to write (25 hours) but pay significantly better ($400 per article). Proofreading is often tedious, but the writer can always find proofreading jobs that pay $20 per hour. The writer wants to maximize her income, but doesn't want to work more than 45 hours per week. Additionally, she dislikes proofreading so she would like to spend no more than 7 hours per week on that task. Both newspaper stories and magazine articles must be completed in the week they are started (HINT: use an integer constraint to be sure that all newspaper and magazine jobs are finished within a week).

What is the optimal mix of jobs for the writer to accept each week? 

N=? P=?

2) 

A plumbing repair company has 4 employees and must choose which of 4 jobs to assign each to (each employee is assigned to exactly one job and each job must have someone assigned).

1. How many decision variables will the linear programming model include? Number of decision variables?

1. How many fixed requirement constraint will the linear programming model include? Number of requirement contraints

3) 

A firm has 4 plants that produce widgets. Plants A, B, and C can each produce 100 widgets per day. Plant D can produce 50 widgets per day. Each day, the widgets produced in the plants must be shipped to satisfy the demand of 3 customers. Customer 1 requires 75 units per day, customer 2 requires 100 units per day, and customer 3 requires 175 units per day. The shipping costs for each possible route are shown in the table below:

The firm needs to satisfy all demand each day, but would like to minimize the total costs.

The objective function for the firm's problem will have how many terms?

4)

A plumbing repair company has 3 employees and must choose which of 3 jobs to assign each to (each employee is assigned to exactly one job and each job must have someone assigned). Each employee can perform each job, but the cost to perform any given job can vary. The following table shows the cost for each employee to perform each job.

Solve this assignment problem in Excel to find the lowest cost solution and answer the following questions:

1. Which employee is assigned to job 1?

  (Click to select)   Employee B   Employee C   Employee A 

1. Which employee is assigned to job 2?

  (Click to select)   Employee B   Employee C   Employee A 

1. Which employee is assigned to job 3?

  (Click to select)   Employee B   Employee C   Employee A 

1. What is the minimum cost to complete all three jobs?

5) 

A firm is attempting to minimize its shipping costs. The firm has 3 factories and must supply the needs of its 3 customers without shortages. Since the firm has no storage facilities, each factory must make daily shipments to its customers. The table below shows the capacity of each factory, the amount required by each customer, and the cost of shipping from each factory to each customer.

Complete the table below to show the quantity shipped from each factory to each customer. (Leave no cells blank - be certain to enter "0" wherever required.)

What is the total cost of meeting customer requirements each day?