Hilo downtown croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. What is the optimal daily profit? a. Formulate a linear programming model for this problem. а. b. Solve the model by using the computer.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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### Chapter 4: Linear Programming Model and Optimal Solutions

#### Problem 4-1

**Context:**

Hilo Downtown Croissant Shop produces two products: bear claws (B) and almond-filled croissants (C).

- **Bear Claw Requirements:**
  - 6 ounces of flour
  - 1 ounce of yeast
  - 2 tablespoons (TS) of almond paste

- **Almond-Filled Croissant Requirements:**
  - 3 ounces of flour
  - 1 ounce of yeast
  - 4 tablespoons (TS) of almond paste

**Available Resources:**
- 6600 ounces of flour
- 1400 ounces of yeast
- 4800 tablespoons of almond paste

**Profits:**
- Bear claw: 20 cents each
- Almond-filled croissant: 30 cents each

**Objective:**
Determine the optimal daily profit.

**Tasks:**

a. **Formulate a Linear Programming Model:**
   - Develop a mathematical model to maximize profits considering the constraints of available resources.

b. **Solve the Model Using a Computer:**
   - Use computational tools to find the optimal solution for production quantities and profit.

This exercise will help understand the application of linear programming in optimizing resource allocation to maximize profits.
Transcribed Image Text:### Chapter 4: Linear Programming Model and Optimal Solutions #### Problem 4-1 **Context:** Hilo Downtown Croissant Shop produces two products: bear claws (B) and almond-filled croissants (C). - **Bear Claw Requirements:** - 6 ounces of flour - 1 ounce of yeast - 2 tablespoons (TS) of almond paste - **Almond-Filled Croissant Requirements:** - 3 ounces of flour - 1 ounce of yeast - 4 tablespoons (TS) of almond paste **Available Resources:** - 6600 ounces of flour - 1400 ounces of yeast - 4800 tablespoons of almond paste **Profits:** - Bear claw: 20 cents each - Almond-filled croissant: 30 cents each **Objective:** Determine the optimal daily profit. **Tasks:** a. **Formulate a Linear Programming Model:** - Develop a mathematical model to maximize profits considering the constraints of available resources. b. **Solve the Model Using a Computer:** - Use computational tools to find the optimal solution for production quantities and profit. This exercise will help understand the application of linear programming in optimizing resource allocation to maximize profits.
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