Tom's, Inc., produces various Mexican food products and sells them to Western Foods, a chain of grocery stores located in Texas and New Mexico. Tom's, Inc., makes two salsa products: Western Foods Salsa and Mexico City Salsa. Essentially, the two products have different blends of whole tomatoes, tomato sauce, and tomato paste. The Western Foods Salsa is a blend of
5
0
%
whole tomatoes,
3
0
%
tomato sauce, and
2
0
%
tomato paste. The Mexico City Salsa, which has a thicker and chunkier consistency, consists of
7
0
%
whole tomatoes,
1
0
%
tomato sauce, and
2
0
%
tomato paste. Each jar of salsa produced weighs
1
0
ounces. For the current production period, Tom's, Inc., can purchase up to
2
8
0
pounds of whole tomatoes,
1
3
0
pounds of tomato sauce, and
1
0
0
pounds of tomato paste; the price per pound for these ingredients is $
0
.
9
6
,
$
0
.
6
4
,
and $
0
.
5
6
,
respectively. The cost of the spices and the other ingredients is approximately $
0
.
1
0
per jar. Tom's, Inc., buys empty glass jars for $
0
.
0
2
each, and labeling and filling costs are estimated to be $
0
.
0
3
for each jar of salsa produced. Tom's contract with Western Foods results in sales revenue of $
1
.
6
4
for each jar of Western Foods Salsa and $
1
.
9
3
for each jar of Mexico City Salsa.
Letting
W
=
jars of Western Foods Salsa
M
=
jars of Mexico City Salsa
Max
1
W
+
1
.
2
5
M
5
W
+
7
M
≤
4
4
8
0
Whole tomatoes
3
W
+
1
M
≤
2
0
8
0
Tomato sauce
2
W
+
2
M
≤
1
6
0
0
Tomato paste
W
,
M
≥
0
include:
-
Spreadsheet Model with Solver setup
-
User Interface
(
be sure to set Object Properties as appropriate
)
-
VBA Code to link Model and Interface
-
VBA
Code for Formatting
-
VBA Code for Error Trapping
Question:
Tom's, Inc., produces various Mexican food products and sells them to Western Foods, a chain of grocery stores located in Texas and New Mexico. Tom's, Inc., makes two salsa products: Western Foods Salsa and Mexico City Salsa. Essentially, the two products have different blends of whole tomatoes, tomato sauce, and tomato paste. The Western Foods Salsa is a blend of
5
0
%
whole tomatoes,
3
0
%
tomato sauce, and
2
0
%
tomato paste. The Mexico City Salsa, which has a thicker and chunkier consistency, consists of
7
0
%
whole tomatoes,
1
0
%
tomato sauce, and
2
0
%
tomato paste. Each jar of salsa produced weighs
1
0
ounces. For the current production period, Tom's, Inc., can purchase up to
2
8
0
pounds of whole tomatoes,
1
3
0
pounds of tomato sauce, and
1
0
0
pounds of tomato paste; the price per pound for these ingredients is $
0
.
9
6
,
$
0
.
6
4
,
and $
0
.
5
6
,
respectively. The cost of the spices and the other ingredients is approximately $
0
.
1
0
per jar. Tom's, Inc., buys empty glass jars for $
0
.
0
2
each, and labeling and filling costs are estimated to be $
0
.
0
3
for each jar of salsa produced. Tom's contract with Western Foods results in sales revenue of $
1
.
6
4
for each jar of Western Foods Salsa and $
1
.
9
3
for each jar of Mexico City Salsa.
Letting
W
=
jars of Western Foods Salsa
M
=
jars of Mexico City Salsa
Max
1
W
+
1
.
2
5
M
5
W
+
7
M
≤
4
4
8
0
Whole tomatoes
3
W
+
1
M
≤
2
0
8
0
Tomato sauce
2
W
+
2
M
≤
1
6
0
0
Tomato paste
W
,
M
≥
0
include:
-
Spreadsheet Model with Solver setup
-
User Interface
(
be sure to set Object Properties as appropriate
)
-
VBA Code to link Model and Interface
-
VBA
Code for Formatting
-
VBA Code for Error Trapping
This is AI generated Response.
Asked by: Test User 100147
Created at: 2025-05-07 16:21:15
Final Answer:
RenderedRaw Text
Did you like this answer?
Certainly! Below is a comprehensive guide to setting up your **Linear Programming (LP) Model** for Tom’s, Inc., including:
1. **Spreadsheet Model with Solver Setup**
2. **User Interface (UI) Design Recommendations**
3. **VBA Code:**
- Model-Interface linking
- Formatting
- Error Trapping
---
## 1. Spreadsheet Model with Solver Setup
**Assumptions:**
- All weights are converted to ounces (1 lb = 16 oz).
- Let \( W \) = Jars of Western Foods Salsa
- Let \( M \) = Jars of Mexico City Salsa
**Decision Variables Table:**
| Cell | Description | Value (to be determined) |
|------|------------------------------|--------------------------|
| B3 | Jars of Western Foods Salsa (W) | 0 (initial guess) |
| B4 | Jars of Mexico City Salsa (M) | 0 (initial guess) |
---
**Parameters Table:**
| Ingredient | Max Pounds | Max Ounces | Western Foods % | Mexico City % |
|-----------------|------------|------------|-----------------|---------------|
| Whole Tomatoes | 280 | 4480 | 50% | 70% |
| Tomato Sauce | 130 | 2080 | 30% | 10% |
| Tomato Paste | 100 | 1600 | 20% | 20% |
---
**Constraints (in ounces):**
| Ingredient | Formula | Cell |
|-----------------|-------------------------------------------|--------|
| Whole Tomatoes | =B3*10*0.5 + B4*10*0.7 ≤ 4480 | B7 |
| Tomato Sauce | =B3*10*0.3 + B4*10*0.1 ≤ 2080 | B8 |
| Tomato Paste | =B3*10*0.2 + B4*10*0.2 ≤ 1600 | B9 |
---
**Objective Function:**
- **Revenue per jar:**
- Western Foods: $1.64
- Mexico City: $1.93
- **Cost per jar:**
- Ingredients (per jar):
- Western Foods: 5 oz tomatoes @ $0.96/lb, 3 oz sauce @ $0.64/lb, 2 oz paste @ $0.56/lb
- Mexico City: 7 oz tomatoes @ $0.96/lb, 1 oz sauce @ $0.64/lb, 2 oz paste @ $0.56/lb
- All: $0.10 (spices), $0.02 (jar), $0.03 (label/filling)
- **Calculate total cost per jar for each type.**
- **Profit per jar:**
- Western Foods: Revenue - Cost
- Mexico City: Revenue - Cost
- **Let’s denote profit per jar as:**
- Western Foods: $X
- Mexico City: $Y
- **Objective:**
- Maximize \( X \cdot W + Y \cdot M \)
**[For simplicity, let's use the coefficients you provided: 1 for W, 1.25 for M, which reflect the profit per jar.]**
---
### **Excel Layout Example**
| | A | B |
|------|-----------------------|-----------|
| 1 | Decision Variables | |
| 2 | Western Foods (W) | 0 |
| 3 | Mexico City (M) | 0 |
| 4 | | |
| 5 | Constraints | Used |
| 6 | Whole Tomatoes (oz) | =B2*5 + B3*7 |
| 7 | Max Allowed | 4480 |
| 8 | Tomato Sauce (oz) | =B2*3 + B3*1 |
| 9 | Max Allowed | 2080 |
| 10 | Tomato Paste (oz) | =B2*2 + B3*2 |
| 11 | Max Allowed | 1600 |
| 12 | | |
| 13 | Objective Function | =1*B2 + 1.25*B3 |
**Set up Solver:**
- Set Objective: **B13** (maximize)
- By Changing: **B2:B3**
- Subject to:
- B6 ≤ B7
- B8 ≤ B9
- B10 ≤ B11
- B2, B3 ≥ 0 (non-negativity)
---
## 2. User Interface (UI) Recommendations
- Use a separate "Interface" sheet.
- Add Input cells for ingredient limits, prices, and profit coefficients (with Data Validation).
- Add "Run Solver" button.
- Display output cells for optimal W, M, and total profit.
- Use form controls (e.g., spin buttons, drop-downs) for user interaction.
---
## 3. VBA Code
### **a. Model-Interface Linking VBA**
```vba
Sub RunSalsaSolver()
' Ensure Solver Add-In is enabled
If Not AddInInstalled("Solver Add-in") Then
MsgBox "Solver Add-in is not installed. Please install it first.", vbCritical
Exit Sub
End If
' Clear previous Solver constraints
SolverReset
' Set up Solver parameters
SolverOk SetCell:="Sheet1!$B$13", MaxMinVal:=1, ValueOf:=0, ByChange:="Sheet1!$B$2:$B$3"
SolverAdd CellRef:="Sheet1!$B$6", Relation:=1, FormulaText:="Sheet1!$B$7"
SolverAdd CellRef:="Sheet1!$B$8", Relation:=1, FormulaText:="Sheet1!$B$9"
SolverAdd CellRef:="Sheet1!$B$10", Relation:=1, FormulaText:="Sheet1!$B$11"
SolverAdd CellRef:="Sheet1!$B$2", Relation:=3, FormulaText:="0"
SolverAdd CellRef:="Sheet1!$B$3", Relation:=3, FormulaText:="0"
' Solve the model
SolverSolve UserFinish:=True
' Format output cells (see formatting code below)
FormatOutputCells
' Error trapping (see error trapping code below)
If Range("Sheet1!$B$2") < 0 Or Range("Sheet1!$B$3") < 0 Then
MsgBox "Solution out of feasible range.", vbCritical
End If
End Sub
Function AddInInstalled(AddInName As String) As Boolean
Dim ai As AddIn
AddInInstalled = False
For Each ai In Application.AddIns
If ai.Name = AddInName Then
AddInInstalled = ai.Installed
Exit Function
End If
Next ai
End Function
```
---
### **b. VBA Code for Formatting**
```vba
Sub FormatOutputCells()
With Range("Sheet1!$B$2:$B$4")
.Interior.Color = RGB(200, 255, 200)
.Font.Bold = True
.NumberFormat = "0"
End With
With Range("Sheet1!$B$13")
.Font.Bold = True
.Font.Color = RGB(0, 100, 0)
.NumberFormat = "$#,##0.00"
End With
End Sub
```
---
### **c. VBA Code for Error Trapping**
```vba
Sub CheckInputErrors()
Dim tomatoes As Double, sauce As Double, paste As Double
tomatoes = Range("Sheet1!$B$7").Value
sauce = Range("Sheet1!$B$9").Value
paste = Range("Sheet1!$B$11").Value
If tomatoes <= 0 Or sauce <= 0 Or paste <= 0 Then
MsgBox "Ingredient maximums must be positive.", vbCritical
Exit Sub
End If
If Range("Sheet1!$B$2") < 0 Or Range("Sheet1!$B$3") < 0 Then
MsgBox "Negative production is not allowed.", vbCritical
Exit Sub
End If
End Sub
```
---
## **How to Use**
1. **Prepare your spreadsheet** per the above design.
2. **Create a button** on your Interface sheet, and assign `RunSalsaSolver` macro.
3. **Enter parameters** in the designated cells.
4. **Click the button** to run Solver, format outputs, and check for errors.
---
**If you need a sample Excel file with this model and code, let me know!**
You can adapt the sheet names and cell references as required. This approach ensures your model is robust, user-friendly, and error-resistant.
VIPSolutions focuses on clear, step‑by‑step explanations so you can learn quickly. Whether you need an AI‑generated walkthrough or a short hint to get unstuck, each solution is organized for fast reading and easy review later.
Search similar questions, compare approaches, and bookmark the best answers for revision. Our goal is simple: quick, reliable study help that feels natural—not noisy.
VIPSolutions