The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker’s, Inc. would like to maximize profits.What is the daily profit when producing the optimal amounts?

Question
Asked Oct 28, 2019

The owner of Crackers, Inc. produces both Deluxe (D) and Classic (C) crackers. She only has 4,800 ounces of sugar, 9,600 ounces of flour, and 2,000 ounces of salt for her next production run. A box of Deluxe crackers requires 2 ounces of sugar, 6 ounces of flour, and 1 ounce of salt to produce. A box of Classic crackers requires 3 ounces of sugar, 8 ounces of flour, and 2 ounces of salt to produce. Profits are 40 cents for a box of Deluxe crackers and 50 cents for a box of Classic crackers. Cracker’s, Inc. would like to maximize profits.

What is the daily profit when producing the optimal amounts?

 

check_circleExpert Solution
Step 1

Introduction:

The given problem is solved using linear programming. The given problem is formulated as shown below:

Let ‘D’ be a box of deluxe crackers.

Let ‘C’ be a box of classic crackers.

 

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Step 2

Excel input and formulas:

 

1 Objective func tion
Delux crackers (D)
Classic crackers () Total pro St
2
3 Number of boses
=SUMPRODUCTB3:C3,B4 : C4)
4 Profit pr box
0.4
05
5
6 Constraints
7Sugar
8 Flour
9Sat
Used resources
Sign Available resources
4300
9600
|2000
-SUMPRODUCTSBS3:SCS387:CT)
|-SUMPRODUCTGB3:SC53B8:CB)
SUMPRODUCTGBS3:SCS3B9:C9) k
2
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1 Objective func tion Delux crackers (D) Classic crackers () Total pro St 2 3 Number of boses =SUMPRODUCTB3:C3,B4 : C4) 4 Profit pr box 0.4 05 5 6 Constraints 7Sugar 8 Flour 9Sat Used resources Sign Available resources 4300 9600 |2000 -SUMPRODUCTSBS3:SCS387:CT) |-SUMPRODUCTGB3:SC53B8:CB) SUMPRODUCTGBS3:SCS3B9:C9) k 2

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Step 3

Solver input:

 

...
Solver Parameters
X
Set Objective:
SDS4
OMin
To:
0
Мах
Value Of:
By Changing Variable Cells:
$BS3:SCS3
Subject to the Constraints:
SDS7:SDS9 <SFS7:SF$9
Add
Change
Delete
Beset All
Load/Save
Make Unconstrained Variables Non-Negative
Simplex LP
Select a Solving
Method:
Options
Solving Method
Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex
engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are
non-smooth.
Solve
Close
Нelp
help_outline

Image Transcriptionclose

Solver Parameters X Set Objective: SDS4 OMin To: 0 Мах Value Of: By Changing Variable Cells: $BS3:SCS3 Subject to the Constraints: SDS7:SDS9 <SFS7:SF$9 Add Change Delete Beset All Load/Save Make Unconstrained Variables Non-Negative Simplex LP Select a Solving Method: Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Solve Close Нelp

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