# Government constraint

Waleed Alrabghi

IE 3530

Homework 2

9/28/2019

1. Go over the San Francisco Police Department Scheduling Problem in your textbook (pp. 7-9). Reorganize the information provided, and clearly explain in a page what needs to be done in every step of the model building process.

2. Section 3.1-Problem 1 (page 55)

Also, (a) Solve the problem in Excel Solver; (b) Clearly explain your decision variables, objective function, objective function coefficients, constraints, technological coefficients, feasible region, and solution.

Weekly revenues

The objective function is Maximize z

Constraint 1

Constraint 2

Constraint 3

The mathematical model of the given LP is Maximize the following equation

Land constraint

Labor constraint

Government constraint

Sign restriction

3. Section 3.1-Problem 2 (page 55)

A) (

Land constraint

Labor constraint

Government constraint

The last constraint is not satisfied, therefore the point 2, 3is not in the feasible region.

B) (

Land constraint

Labor constraint

Government constraint

The Second constraint is not satisfied, therefore the point 4,3 is not in the feasible region.

C)

One value is negative, non-negative restriction is not satisfied. It can be concluded that the point (2,-1) is not in the feasible region.

D) (

Land constraint

Labor constraint

Government constraint

All constraints and non-negative restrictions are satisfied, therefore the point 3,2 is in the feasible region.

4. Section 3.1-Problem 3 (Note: 1 bushel of corn uses 1/10 acre of land and 4/10 hours of labor while 1 bushel of wheat uses 1/25 acre of land and 10/25 hours of labor. (page 55)

Also: (a) Solve the problem in Excel Solver and upload your Excel file; (b) Clearly explain your decision variables, objective function, objective function coefficients, constraints, technological coefficients, feasible region, and solution, (c) Compare your solution with Question 2.

Constraint 1: Seven acers of land is available

Constraint 2: Forty hours per week of labor available

Constraint 3: At least 30 bushels of corn be produced

10

5. Section 3.2-Problem 1 (page 63)

The vertices of the feasible region are H(3,0), B(7,0), C(5,2) and G(3,2.8).

The values of the objective function at these points are 90, 210, 350, and 370. Since the maximum value of z is at 3,2.80. Therefore, the optimal solution of given LP is The graph is attached down . 