linear programming model to compute an optimal production policy

Part I
During the next four months Shoeco must meet, on time, the following demands for pairs of shoes: 300 in month 1; 500 in month 2; 100 in month 3; and 100 in month 4. At the beginning of month 1, 50 pairs of shoes are on hand, and Shoeco has three workers. A worker is paid $1500 per month. Each worker can work up to 160 hours a month before he or she receives overtime. A worker may be required to work up to 20 hours of overtime and is paid $25 per hour for overtime. It takes four hours of labor and $5 of raw material to produce a pair of shoes. At the beginning of each month workers can be hired or fired. Hiring costs are $1600 per worker and firing costs are $2000 per worker. At the end of each month, a holding cost of $30 is charged for each pair left in inventory. Production in a given month can be used to meet that months demand. Use LP to determine an optimal production and labor policy.

Part II
Assuming backlogs are allowed and that it costs $25 for each pair backlogged, adjust the above model to include that aspect.

The key to this problem is realizing that there are two variables to solve: the number of workers and the number of hours of overtime. Solver accommodates allowing two variables. Here is the set-up in excel. Look at the formulas in the cells to get a grasp of ...

Solution Summary

The solution presents explanations and calculations to arrive at an optimal production policy.

A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows.
Hours/Unit
Product Line 1 Line 2
A 12 4
B 4

Problem:
Richland Manufacturing Company manufactures solid oak computer desks on two separate production lines at its plant in Richland, Vermont. Production line 1 is continuously operated and is staffed with workers experienced in the construction of quality oak furnishings. Production line 2 is activated only when demand is

Linearprogramming
Items X1 X2
Profit per Item 3 6
Resource constraints Available Usage Left over
1 7 3 40 0 40
Output
X1= 0
X2= 0
Z= 0
Solve the following linearprogrammingmodel by using the computer
Minimi

Consider the following linear programming problem.
MIN Z = 10x1 + 20x2
Subject to: x1 + x2 >= 12
2x1 + 5x2 >= 40
x1, x2 >= 0
What is minimum cost Z=??
Put your answer in the xxx.x (to one decimal place)

I need assistance in starting and developing the linear equation. I am so lost.
The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labor utilization, labor productivity and product profitability.
Pro

Homework problems. File is attached.
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True/False
Indicate whether the sentence or statement is true or false.
______ 1. A linearprogrammingmodel consists of decision variables, constraints, but no objective function.
______ 2. Linearprogrammingmodels exhibit linearity among all constraint relationships and th

Plant Equipment Corporation (PEC) manufactures two large industrial machines--a metal compactor and a drill press. Next month PEC will convert its production facilities to produce new machine designs and will cease producing the current models.
PEC must determine its production schedule for this month, however, PEC could sel

1. Integer Programming Problem
Consider the following integer linearprogramming problem
Max Z=3x1+2x2
Subject to:
3x1+5x2<=30
5X1+2x2<=28
x1<=8
x1,x2>=0 and integer
The solution to the Linearprogramming relaxation is: x1 = 5.714, x2= 2.571.
What is the Z value for the optimal solution under integer