LP Problem & ranges of optimality

[prettyish]

After looking at the book for well over 2 hours I am still no closure to an answer. I think if someone could show me how to do A & D I can do the rest. Thanks in advance!

Answer Questions 2 and 3 based on the following LP problem.

Let C = number of clocks to be produced
R = number of radios to be produced
T = number of toasters to be produced

Maximize 8C + 10R + 7T Total profit
Subject to
7C + 10R + 5T ? 2000 Production budget constraint
2C + 3R + 2T ? 660 Labor hours constraint
C ? 200 Maximum demand for clocks constraint
R ? 200 Maximum demand for radios constraint
T ? 200 Maximum demand for toasters constraint
And C, R, T ? 0 Non-negativity constraints

The QM for Windows output for this problem is given below.

Linear Programming Results:
Variable Status Value
C Basic 175
R NONBasic 0
T Basic 155
slack 1 NONBasic 0
slack 2 NONBasic 0
slack 3 Basic 25
slack 4 Basic 200
slack 5 Basic 45
Optimal Value (Z) 2485

Original Problem with answers:
C R T RHS Dual
Maximize 8 10 7
Constraint 1 7 10 5 <= 2000 .5
Constraint 2 2 3 2 <= 660 2.25
Constraint 3 1 0 0 <= 200 0
Constraint 4 0 1 0 <= 200 0
Constraint 5 0 0 1 <= 200 0
Solution-> 175 0 155 Optimal Z-> 2485

Ranging Results:
Variable Value Reduced Cost Original Val Lower Bound Upper Bound
C 175 0 8 7 9.8
R 0 1.75 10 -Infinity 11.75
T 155 0 7 5.7143 8

Constraint Dual Value Slack/Surplus Original Val Lower Bound Upper Bound
Constraint 1 .5 0 2000 1910 2050
Constraint 2 2.25 0 660 640 685.7143
Constraint 3 0 25 200 175 Infinity
Constraint 4 0 200 200 0 Infinity
Constraint 5 0 45 200 155 Infinity

 

[mmm4444bot]

... show me how to do A & D ...

Tell me what A & D are, first.

Perhaps, after I see what these questions are, I will be able to show you something.

~ Mark

 

[prettyish]

2. (a) Determine the optimal solution and the optimal value from the computer output given above and interpret their meanings.
(b) Determine the slack (or surplus) value for each constraint from the computer output given above and interpret its meaning.


3. (a) What are the ranges of optimality for the profit of a clock, a radio, and a toaster?
(b) Find the dual prices of the five constraints and interpret their meanings. What are the ranges in which these dual prices are valid?
(c) Which resource should be obtained in larger quantity to increase the profit most? (Note: answer this without solving the problem again).
(d) If the profit contribution of a clock changes from $8 to $7.50, what will be the new optimal solution? What will be the new total profit? (Note: answer this without solving the problem again).