LP Setup and Interpretation
The Syflansyd Nut Company has enjoyed booming sales following the success of its "Sometimes You Feel Like a Nut, Sometimes You Don't" advertising campaign. Syflansyd packages and sells four types of nuts in four different types of mixed-nut packages. These products include bulk (B), economy (E), fancy (F), and regular (R) mixed-nut packages. Each of these packages contains a different mixture of almonds (A), cashews (C), filberts (F), and peanuts (P). Based on its contracts with current suppliers, the company has the following daily inventory of each of the following nuts: almonds, 8,000 ounces; cashews, 7,000 ounces; filberts, 7,500 ounces; and peanuts, 10,000 ounces.
Given available inventory, it is management's goal to maximize profits by offering the optimum mix of the four package types. Profit earned per package type is as follows:
|
Bulk
|
$0.50
|
|
Economy
|
$0.25
|
|
Fancy
|
$1.25
|
|
Regular
|
$0.75
|
|
The composition of each of the four package types can be summarized as follows:
|
|
|
|
Ounces per Package
|
|
|
Bulk
|
Economy
|
Fancy
|
Regular
|
|
Almonds
|
35
|
2
|
3
|
2
|
|
Cashews
|
35
|
1
|
4
|
2
|
|
Filberts
|
35
|
1
|
3
|
2
|
|
Peanuts
|
35
|
8
|
2
|
6
|
|
Total
|
140
|
12
|
12
|
12
|
Solution values for the optimal number of packages to produce (decision variables) and excess capacity (slack variables) are the following:
B = 0
E = 0
F = 1,100
R = 1,300
SA = 2,100
SC = 0
SF = 1,600
SP = 0
A. Identify and interpret the appropriate Syflansyd objective function.
B. Using both inequality and equality forms, set up and interpret the resource constraints facing the Syflansyd Company.
C. Calculate optimal daily profit, and provide a complete interpretation of the full solution to this linear programming problem.