# Linear equation: Q4

#### San1998

##### New member
Q4:
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. Use the output to answer these questions.
MAX 4X1+6X2+7X3
S.T.
1) 3X1+2X2+5X3 <120
2) 1X1+3X2+3X3 <80
3) 5X1+5X2+8X3 <160
4) +1X3 >10
OPTIMAL SOLUTION
Objective Function Value = 166.000
Variable Value Reduced Cost
X1 0.000 2.000
X2 16.000 0.000
X3 10.000 0.000
Constraint Slack/Surplus Dual Price
1 38.000 0.000
2 2.000 0.000
3 0.000 1.200
4 0.000 −2.600
OBJECTIVE COEFFICIENT RANGES
Variable Lower Limit Current Value Upper Limit
X1 No Lower Limit 4.000 6.000
X2 4.375 6.000 No Upper Limit
X3 No Lower Limit 7.000 9.600
RIGHT HAND SIDE RANGES
Constraint Lower Limit Current Value Upper Limit
1 82.000 120.000 No Upper Limit
2 78.000 80.000 No Upper Limit
3 80.000 160.000 163.333
4 8.889 10.000 20.000
a. How much of ingredient 1 will be put into the blend?
b. How much of ingredient 2 will be put into the blend?
c. How much of ingredient 3 will be put into the blend?
d. How much resource A is used?
e. How much resource B will be left unused?
f. What will the profit be?
g. What will happen to the solution if the profit from ingredient 2 drops to 4?
h. What will happen to the solution if the profit from ingredient 3 increases by 1?
i. What will happen to the solution if the amount of resource C increases by 2?
j. What will happen to the solution if the minimum requirement for ingredient 3 increases to
15?

#### Jomo

##### Elite Member
So what have you tried? Where are you stuck? Have you read the guidelines for this forum. If not, then please do so.

#### San1998

##### New member
Hi,
I don't really know how to solve this type of problems in which raw data is given. The curriculum which I'm studying mainly deals with simple product mix linear equation problems in which we have to use corner point method or isoprofit line. I did search this question online to try and obtain the methodology but I didn't have any luck. I don't know how to solve this problem. I know this isn't a free homework help group, but please do know that my course contains no relevant study material to help with this.

#### Jomo

##### Elite Member
Actually this IS a free homework help group. The key word is help. We help student arrive at the correct answer by giving leading hints.
You must have tried something, like maybe graphing the constraints? Please show us something so we can move you along to the solution.