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Problem 9-05 (Algorithmic) Kilgore’s Deli is a small delicatessen located near a major university. Kilgore’s does a large walk-in carry-out lunch business. The deli offers two luncheon...

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  1. Problem 9-05 (Algorithmic)

Kilgore’s Deli is a small delicatessen located near a major university. Kilgore’s does a large walk-in carry-out lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The profit on one serving of Wimpy is $0.4, on one serving of Dial 911, $0.53. Each serving of Wimpy requires 0.2 pound of beef, 0.2 cup of onions, and 5 ounces of Kilgore’s special sauce. Each serving of Dial 911 requires 0.2 pound of beef, 0.35 cup of onions, 2 ounces of Kilgore’s special sauce, and 5 ounces of hot sauce. Today, Kilgore has 15 pounds of beef, 10 cups of onions, 84 ounces of Kilgore’s special sauce, and 55 ounces of hot sauce on hand.

    1. Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial 911 to make in order to maximize his profit today. If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

Let

W = number of servings of Wimpy to make

 

D = number of servings of Dial 911 to make

Max

W

+

D

 

 

 

s.t.

 

 

 

 

 

 

 

W

+

D

 

(Beef)

 

W

+

D

 

(Onions)

 

W

+

D

 

(Special Sauce)

 

W

+

D

 

(Hot Sauce)

 

 

 

W, D

0

 

          
    1. Find an optimal solution. If required, round your answers to two decimal places.

      W = , D = , Profit = $
    2. What is the shadow price for special sauce? If required, round your answers to two decimal places.

      $

      Interpret the shadow price.

      The input in the box below will not be graded, but may be reviewed and considered by your instructor.

    3. Increase the amount of special sauce available by 1 ounce and re-solve. If required, round your answers to two decimal places.

      W = , D = , Profit = $

      Does the solution confirm the answer to part (c)?

 

Answered Same DayNov 02, 2019

Solution

David answered on Nov 30 2019
61 Votes
a,b,c
    objective func:
    max    10.79
    decision func:
    W    12.4
    D    11
    constraint:
    4.68    <=    15    beef
    6.33    <=    10    onions
    84    <=    84    special sause
    55    <=    55    hot sause
    12.4    >=    0
    11    >=    0
Answer Report 2
    Microsoft Excel 15.0 Answer Report
    Worksheet: [Book2]d
    Report Created: 11/3/2017 3:47:59 PM
    Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
    Solver Engine
        Engine: Simplex LP
        Solution Time: 0.063 Seconds.
        Iterations: 4 Subproblems: 0
    Solver Options
        Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling
        Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative
    Objective Cell (Max)
        Cell    Name    Original Value    Final Value
        $B$2    max    10.79    10.87
    Variable Cells
        Cell    Name    Original Value    Final Value    Intege
        $B$5    W    12.4    12.6    Contin
        $B$6    D    11    11    Contin
    Constraints
        Cell    Name    Cell Value    Formula    Status    Slack
        $A$13    constraint:    12.6    $A$13>=$C$13    Not Binding    12.6
        $A$14    constraint:    11    $A$14>=$C$14    Not Binding    11
        $A$9    constraint:    4.72    $A$9<=$C$9    Not Binding    10.28
        $A$10    constraint:    6.37    $A$10<=$C$10    Not Binding    3.63
        $A$11    constraint:    85    $A$11<=$C$11    Binding    0
        $A$12    constraint:    55    $A$12<=$C$12    Binding    0
Sensitivity Report 2
    Microsoft Excel 15.0 Sensitivity Report
    Worksheet: [Book2]d
    Report...
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