Are my formulas correct and did I get the correct answer (I get $333,000 as my answer for Maximized Profit)? If not show me how to fix it. Question: Sunblessed Juice Company sells bags of oranges and cartons of orange juice. Sunblessed grades oranges on a scale of 1 (poor) to 10 (excellent). At present, Sunblessed has 220,000 pounds of grade 6 oranges and 150,000 pounds of grade 9 oranges on hand. The aver- age quality of oranges sold in bags must be at least 7, and the average quality of the oranges used to produce orange juice must be at least 8. Each pound of oranges that is used for juice yields a revenue of $2.25 and in- curs a variable cost (consisting of labor costs, variable overhead costs, inventory costs, and so on) of $1.35. Each pound of oranges sold in bags yields a revenue of $2.00 and incurs a variable cost of $1.20. a.    Determine how Sunblessed can maximize its profit.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Are my formulas correct and did I get the correct answer (I get $333,000 as my answer for Maximized Profit)? If not show me how to fix it.

Question: Sunblessed Juice Company sells bags of oranges and cartons of orange juice. Sunblessed grades oranges on a scale of 1 (poor) to 10 (excellent). At present, Sunblessed has 220,000 pounds of grade 6 oranges and 150,000 pounds of grade 9 oranges on hand. The aver- age quality of oranges sold in bags must be at least 7, and the average quality of the oranges used to produce orange juice must be at least 8. Each pound of oranges that is used for juice yields a revenue of $2.25 and in- curs a variable cost (consisting of labor costs, variable overhead costs, inventory costs, and so on) of $1.35. Each pound of oranges sold in bags yields a revenue of $2.00 and incurs a variable cost of $1.20.

a.    Determine how Sunblessed can maximize its profit.

### Selling Oranges and Orange Juice: A Cost and Profit Analysis

This spreadsheet is a detailed analysis of costs, revenue, and profitability associated with selling oranges as juice and in bags. Below is an explanation of each section and the calculations performed.

#### 1. Revenues and Variable Costs
- **Juice**:
  - Revenue per unit: \$2.25
  - Variable cost per unit: \$1.35
- **Bags**:
  - Revenue per unit: \$2.00
  - Variable cost per unit: \$1.20

#### 2. Grades Used to Make Juice and Bags
- Grade 6 orange allocations:
  - For Juice: 220,000 units
  - For Bags: 0 units
- Grade 7 orange allocations:
  - For Juice: 150,000 units
  - For Bags: 0 units
- Total oranges used for juice: SUM(B10:B11) = 220,000 + 150,000 = 370,000 units

Oranges available:
- Grade 6: 220,000 units
- Grade 7: 150,000 units

#### 3. Required Average Quality
- Average quality required for:
  - Juice: 8
  - Bags: 7

#### 4. Quality Constraints
**Actual Quality Calculation**:
- Juice: `=SUMPRODUCT(A10:A11, B10:B11)/SUM(B10:B11)`

Required units based on quality:
- For Juice: `=B12*B16`
- For Bags: `=C12*C16`

#### 5. Cost and Revenue Calculations
- **Total Variable Cost**:
  - Juice: `=B12*B6 + C12*C6`
  - Bags: `=B12*1.35 + C12*1.20`

- **Total Revenue**:
  - Juice: `=B12*B5 + C12*C5`
  - Bags: `=B12*2.25 + C12*2`

#### 6. Maximized Profit
The maximized profit is calculated by subtracting the total variable cost from the total revenue:
- `=B25-B24`

In the spreadsheet, specific calculations and logical formulas have been utilized to manage the resources effectively to maximize profit while maintaining required quality standards. This is crucial for making informed business decisions in the farming and
Transcribed Image Text:### Selling Oranges and Orange Juice: A Cost and Profit Analysis This spreadsheet is a detailed analysis of costs, revenue, and profitability associated with selling oranges as juice and in bags. Below is an explanation of each section and the calculations performed. #### 1. Revenues and Variable Costs - **Juice**: - Revenue per unit: \$2.25 - Variable cost per unit: \$1.35 - **Bags**: - Revenue per unit: \$2.00 - Variable cost per unit: \$1.20 #### 2. Grades Used to Make Juice and Bags - Grade 6 orange allocations: - For Juice: 220,000 units - For Bags: 0 units - Grade 7 orange allocations: - For Juice: 150,000 units - For Bags: 0 units - Total oranges used for juice: SUM(B10:B11) = 220,000 + 150,000 = 370,000 units Oranges available: - Grade 6: 220,000 units - Grade 7: 150,000 units #### 3. Required Average Quality - Average quality required for: - Juice: 8 - Bags: 7 #### 4. Quality Constraints **Actual Quality Calculation**: - Juice: `=SUMPRODUCT(A10:A11, B10:B11)/SUM(B10:B11)` Required units based on quality: - For Juice: `=B12*B16` - For Bags: `=C12*C16` #### 5. Cost and Revenue Calculations - **Total Variable Cost**: - Juice: `=B12*B6 + C12*C6` - Bags: `=B12*1.35 + C12*1.20` - **Total Revenue**: - Juice: `=B12*B5 + C12*C5` - Bags: `=B12*2.25 + C12*2` #### 6. Maximized Profit The maximized profit is calculated by subtracting the total variable cost from the total revenue: - `=B25-B24` In the spreadsheet, specific calculations and logical formulas have been utilized to manage the resources effectively to maximize profit while maintaining required quality standards. This is crucial for making informed business decisions in the farming and
### Excel Solver Parameters: Setup and Usage

Excel's Solver tool is a powerful data analysis feature designed to find optimal solutions for decision-making problems. Below is a detailed breakdown of the Solver Parameters window setup and elements.

#### Solver Parameters Window Breakdown

**Set Objective:**
- This field is used to specify the target cell (often known as the objective cell) where the result of the objective function will be displayed.
- In the provided screenshot, the objective cell is set to `$B$27`.

**To:** 
- Options available are either `Max`, `Min`, or a specific `Value Of`. These define whether the objective is to maximize, minimize, or set the objective cell to a specific value.
- Here, the option selected is `Max`, meaning the Solver will aim to maximize the value in cell `$B$27`.

**By Changing Variable Cells:**
- This field specifies the range of cells that Solver can adjust to optimize the objective.
- Range given in the example is `$B$10:$C$11`.

**Subject to the Constraints:**
- Constraints are conditions that must be met for the solution to be valid.
- Two constraints are defined:
  1. `$B$20:$C$20 >= $B$22:$C$22`
  2. `$D$10:$D$11 <= $F$10:$F$11`

**Additional Options:**
- Add, Change, and Delete buttons allow you to manage the constraints.
- `Make Unconstrained Variables Non-Negative` checkbox is selected to ensure all variables remain non-negative.
- `Select a Solving Method:` dropdown menu provides three options:
  1. GRG Nonlinear
  2. Simplex LP (Selected in this screenshot)
  3. Evolutionary

**Solving Method Description:**
- Below the dropdown, there's a brief explanation to help users select the appropriate solving method based on their problem type. For linear problems, the LP Simplex engine is recommended, while the other options are suitable for non-linear and non-smooth problems.

**Action Buttons:**
- `Reset All`: Clears all current settings.
- `Load/Save`: Allows for previous setups to be loaded or current setups to be saved.
- `Options`: Launches additional settings that the user can adjust.
- `Solve`: Starts the Solver process to find the optimal solution.
- `Close`: Exits the Solver Parameters window without running the
Transcribed Image Text:### Excel Solver Parameters: Setup and Usage Excel's Solver tool is a powerful data analysis feature designed to find optimal solutions for decision-making problems. Below is a detailed breakdown of the Solver Parameters window setup and elements. #### Solver Parameters Window Breakdown **Set Objective:** - This field is used to specify the target cell (often known as the objective cell) where the result of the objective function will be displayed. - In the provided screenshot, the objective cell is set to `$B$27`. **To:** - Options available are either `Max`, `Min`, or a specific `Value Of`. These define whether the objective is to maximize, minimize, or set the objective cell to a specific value. - Here, the option selected is `Max`, meaning the Solver will aim to maximize the value in cell `$B$27`. **By Changing Variable Cells:** - This field specifies the range of cells that Solver can adjust to optimize the objective. - Range given in the example is `$B$10:$C$11`. **Subject to the Constraints:** - Constraints are conditions that must be met for the solution to be valid. - Two constraints are defined: 1. `$B$20:$C$20 >= $B$22:$C$22` 2. `$D$10:$D$11 <= $F$10:$F$11` **Additional Options:** - Add, Change, and Delete buttons allow you to manage the constraints. - `Make Unconstrained Variables Non-Negative` checkbox is selected to ensure all variables remain non-negative. - `Select a Solving Method:` dropdown menu provides three options: 1. GRG Nonlinear 2. Simplex LP (Selected in this screenshot) 3. Evolutionary **Solving Method Description:** - Below the dropdown, there's a brief explanation to help users select the appropriate solving method based on their problem type. For linear problems, the LP Simplex engine is recommended, while the other options are suitable for non-linear and non-smooth problems. **Action Buttons:** - `Reset All`: Clears all current settings. - `Load/Save`: Allows for previous setups to be loaded or current setups to be saved. - `Options`: Launches additional settings that the user can adjust. - `Solve`: Starts the Solver process to find the optimal solution. - `Close`: Exits the Solver Parameters window without running the
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