Here is a linear programming model where the decision variables represent the amounts of ingredients 1, 2, and 3 to put into a blend. The objective function represents profit. The first three constraints measure the usage and availability of resources A, B, and C. The fourth constraint is a minimum requirement for ingredient 3. Max 5X1 + 6X2 + 7X3 s.t. 2X1 + 2X2 + 5X3 ≤ 120 X1 + 3X2 + 3X3 ≤ 80 4X1 + 5X2 + 8X3 ≤ 160 X3 ≥ 10 Here are screenshots of the Answer Report and the Sensitivity Report for this problem: Use these reports to answer the following questions.Use these reports to answer the following questions.

1. How much of ingredient 1 will be put into the blend?

1. How much of ingredient 2 will be put into the blend?

1. How much of ingredient 3 will be put into the blend?

1. How much resource A is used?

1. How much resource B will be left unused?

1. What will the profit be?

1. What will happen to the solution if the profit from ingredient 2 drops to 4?

1. What will happen to the solution if the profit from ingredient 3 increases by 4?

1. What will happen to the solution if the amount of resource C increases by 20?

1. What will happen to the solution if the minimum requirement for ingredient 3 increases to 15?
    
    

Transcribed Image Text:

Objective Cell (Max) Cell $C$14 Objective Function Variable Cells Cell $B$10 X1 $B$11 X2 $B$12 X3 Constraints Cell $B$18 A $B$19 B $B$20 C $B$21 Min X3 Name Name Name Original Value 18 Original Value 1 1 1 Final Value Cell Value 170 Final Value Integer 20 Contin O Contin 10 Contin Formula Status Slack 90 $B$18<-$D$18 Not Binding 30 50 $B$19<=$D$19 Not Binding 30 160 $B$20<=$D$20 Binding 0 10 $B$21>=$D$21 Binding 0 Objective Cell (Max) Cell $C$14 Objective Function Variable Cells Cell $B$10 X1 $B$11 X2 $B$12 X3 Constraints Cell $B$18 A $B$19 B $B$20 C $B$21 Min X3 Name Name Name Original Value 18 Original Value 1 1 1 Final Value Cell Value 170 Final Value Integer 20 Contin O Contin 10 Contin Formula Status Slack 90 $B$18<-$D$18 Not Binding 30 50 $B$19<=$D$19 Not Binding 30 160 $B$20<=$D$20 Binding 0 10 $B$21>=$D$21 Binding 0

Answer rating: 100% (QA)

1 How much of ingredient 1 will be put into the blend Looking at the Answer Report we see that the optimal solution is X1 40 2 How much of ingredient ... View the full answer