Min 2x, 3x. 1x 125 Demand for product 1x1 1x2 e 350 Total production requirement
ID: 3123731 • Letter: M
Question
Min 2x, 3x. 1x 125 Demand for product 1x1 1x2 e 350 Total production requirement 2xi s 600 Processing time limitation 20 The Management Scientist solution is shown in Figure 8.12. a. What is the optimal solution and what is the minimum production cost? b. specify the range of optimality for the objective function coefficients. c. What are the dual prices for each constraint? Interpret each. d. If total production requirement were increased from 350 to 450 gallons, the the how would value of the optimal solution change? e. Identify the range of feasibility for the right-hand-side values. ure 8.12 THE MANAGEMENT SCIENTIST SOLUTION FOR THE M&D; CHEMICALS PROBLEM objective Function Value 800.000 Variable Value Reduced Costs X1 250.000 0.000 100.000 0.000 Constraint slack/surplus Dual Prices 125.000 0.000 0.000 4.000 0.000 1.000 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit X1 No Lower Limit 2.000 3.000 2.000 3.000 No Upper Limit RIGHT HAND SIDE RANGES constraint Lower Limit current value Upper Limit No Lower Limit 125.000 250.000 300.000 350.000 475.000 475.000 600.000 700.00Explanation / Answer
5.
a) THE OPTIMAL SOLUTION IS
X1 = 250 AND X2 = 100.
MINIMUM PRODUCTION COST = 800
b) Range of optimality
For variable X1 - It has no lower limit and upper limit is 3
For variable X2 - It has a lower limit of 2 and no upper limit
c) The dual price of constraint 1 is 0.00
The dual price of constraint 2 is -4.00
The dual price of constraint 3 is 1.00
Explanation.
The dual price on the constraint 1 is 0. It says that the objective function value — the net cost per day — could be increased by 0 if the demand for product 1 is increased by one each day.
The dual price of the constraint 2 is -4.00 It says that the objective function value — the net cost per day — could be increased by -4.00 or decreased to 4.00 if total production requirement is increased by one each day.
The dual price of the constraint 3 is 1.00 It says that the objective function value — the net cost er day — could be increased by 1.00 if processing time is increased to one unit each day.