Linear programming and sensitivity analysis

1. The binding constraints for this problem are the first and second.

Min x1 + 2X2

s.t. x1 + x2> 300

2x1 + x2> 400

2x1 + 5x2> 750

x1, x2 > 0

a. Keeping cf2 fixed at 2, over what range can cf1 vary before there is a change in the optimal solution point?

b. Keeping cf1 fixed at 1, ovber what range can cf2 vary before there is a change in the optimal solution point?

c. Find the dual price for each constraint.

2. Super City Discount Department Store is open 24 hours a day. The number of cashiers need in each four hour period of the day is listed below.

Period Cashiers Needed

10 p.m. to 2 a.m. 8
2a.m. to 6 a.m. 4
6a.m. to 10 a.m. 7
10a.m. to 2 p.m. 12
2p.m. to 6 p.m. 10
6pm to 10 p.m. 15

If cashiers work for eight consecutive hours, how many should be scheduled to begin working in each period in order to minimize the number of cashiers needed?

Write a Linear Programming Model with objctive function and constraints?

Let TNP= The number if cashiers who begin working at 10 p.m.
TWA= The number of cashiers who begins working at 2 a.m.
SXA= The number of cashiers who begins working at 6 a.m.
TNA= The number of cashiers who begins working at 10 a.m.
TWP= The number of cashiers who begins working at 2 p.m.
SXP= The number of cashiers who begins working at 6 p.m.

3. Island Waters Sports is a business that provides rental equipment and instrution for a variety of water sports in a resort town. On one particular morning, a decision must be made of many Wildlife Raft Trips and how many Group Sailing Lessons should be accommodate six passengers. The revenue per raft is $120. Ten rafts are available, and at least 30 people are on the list for reservations this morning. Each Group Sailing Lesson requires one captain and two crew people for instruction. Two boats are needed for each group. Four students form each group. There are 12 sailboats available, and at least 20 people are on the list for sailing instruction this morining. The revenue per group sailing leaaon is $160. The company would like to minimize the number of customers served while generating at least $1800 in revenue and honoring all reservations.

Let R= The number of Wildlfe Raft Trips to schedule.
S= The numbet of Group Sailing Lessons to schedule

Write a Linear Programming Model with object fuction and constraints.

4. Canning Transport is to move goods from three factories to three distribution centers. Information about the move is given below.

Give the network model and the linear programming model for this problem.

Source Supply Destination Demand

A. 200 X 50
B. 100 Y 125
C. 150 Z 125

Shipping cost are:

Source X Y Z

A. 3 2 5
B. 9 10 --
C. 5 6 4
(Source B cannot ship to destination Z)