Problems:
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1)Enter answers to numbered questions using online Assessment form (untimed one).
2)Upload the spreadsheets you used in solving the questions on this assessment (no spreadsheet needed for questions 38-44) to the online Assignment form that is supposed to go with this. If you cannot upload the spreadsheets, email them to me. Much preferred for you to just upload them.
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CONTACT PROF IF YOU HAVE QUESTIONS
Given the following Solver output what range of values can the objective function coefficient for variable X1 assume without changing the optimal solution?
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Changing Cells
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Final
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Reduced
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Objective
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Allowable
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Allowable
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Cell
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Name
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Value
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Cost
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Coefficient
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Increase
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Decrease
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$B$4
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Number to make: X1
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9.49
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0
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5
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1.54
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1
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$C$4
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Number to make: X2
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1.74
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0
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6
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1.5
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1.47
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Constraints
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Final
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Shadow
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Constraint
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Allowable
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Allowable
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Cell
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Name
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Value
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Price
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R.H. Side
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Increase
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Decrease
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$D$8
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Used
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42
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0
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48
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1E+30
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6
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$D$9
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Used
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132
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0.24
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132
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12
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12
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$D$10
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Used
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24
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1.24
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24
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1.33
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2
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Give answers with two digits to the right of the decimal point, e.g. 1.00
Q1. Bottom of range
Q2. Top of range
Consider the following linear programming model and Solver output. What is the optimal objective function value if the RHS of the first constraint increases to 18? (Give answer with one digit to right of decimal point, e.g., 1.0)
MAX: 7 X1 + 4 X2
Subject to: 2 X1 + X2 £ 16
X1 + X2 £ 10
2 X1 + 5 X2 £ 40
X1, X2 ³ 0
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Changing Cells
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Final
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Reduced
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Objective
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Allowable
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Allowable
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Cell
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Name
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Value
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Cost
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Coefficient
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Increase
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Decrease
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$B$4
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Number to make: X1
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6
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0
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7
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1
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3
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$C$4
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Number to make: X2
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4
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0
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4
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3
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0.5
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Constraints
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Final
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Shadow
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Constraint
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Allowable
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Allowable
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Cell
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Name
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Value
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Price
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R.H. Side
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Increase
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Decrease
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$D$8
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Used
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16
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3
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16
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4
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2.67
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$D$9
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Used
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10
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1
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10
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1
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2
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$D$10
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Used
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32
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0
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40
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1E+30
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8
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Q3. Optimal objective function value =
The Happy Pet pet food company produces dog and cat food. Each food is comprised of meat, soybeans and fillers. The company earns a profit on each product but there is a limited demand for them. The pounds of ingredients required and available, profits and demand are summarized in the following table. The company wants to plan their product mix, in terms of the number of bags produced, in order to maximize profit .
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Product
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Profit per Bag ($)
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Demand for product
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Pounds of Meat per bag
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Pounds of Soybeans per bag
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Pounds of Filler per bag
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Dog food
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4
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40
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4
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6
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4
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Cat food
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5
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30
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5
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3
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10
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Material available (pounds)
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100
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120
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160
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Formulate the LP model for this problem, assuming decision variables are:
X1 = bags of Dog food to produce
X2 = bags of Cat food to produce
Give WHOLE NUMBERS for answers to the questions relating to this LP (e.g.2)
What values are in the constraint for meat (___x1 +___x2 <= ___)?
Q4. LHS coefficient for x1
Q5. LHS coefficient for x2
Q6 RHS value
What is the constraint for soybeans?
Q7. LHS coefficient for x1
Q8. LHS coefficient for x2
Q9 RHS value
What is the constraint for Filler?
Q10. LHS coefficient for x1
Q11. LHS coefficient for x2
Q12 RHS value
What is the constraint for Dog food demand?
Q13. LHS coefficient for x1
Q14 LHS coefficient for x2
Q15 RHS value
What is the constraint for Cat food demand?
Q16. LHS coefficient for x1
Q17. LHS coefficient for x2
Q18RHS value
What is are the objective function coefficients
Q19 For x1
Q20 For x2
Q21 What is the optimal objective function value