### Objective Function for Maximizing Total Revenue#### Problem Statement:For the following problem, what would be the objective function that aims at maximizing the total revenue considering that X1, X2, X3, and X4 are the number of units produced and sold of Products 1, 2, 3, and 4, respectively?#### Data Table:The table below contains the cost per hour for different machines, the manufacturing time required for each product by each machine, and the machine capacities in hours.**Manufacturing Time (hr) per unit**| Machine | Cost per hr ($) | Product 1 | Product 2 | Product 3 | Product 4 | Capacity (hr) || --- | --- | --- | --- | --- | --- | --- || 1 | 10 | 2 | 3 | 4 | 2 | 500 || 2 | 5 | 2 | 1 | 1 | 1 | 380 || 3 | 4 | 7 | 3 | 2 | 1 | 450 |**Unit Selling Price ($)**| Product 1 | Product 2 | Product 3 | Product 4 || --- | --- | --- | --- || 75 | 70 | 55 | 45 |#### Question:What is the correct objective function to maximize the total revenue?#### Multiple Choice Options:- a. 12X1 + 8X2 + 7X3 + 5X4- b. None of the answers- c. 20X1 + 30X2 + 40X3 + 20X4- d. 75X1 + 70X2 + 55X3 + 45X4#### Answer:The correct objective function is:**d. 75X1 + 70X2 + 55X3 + 45X4**This choice reflects the revenue generated by each product based on their unit selling price.#### Explanation:The objective function is constructed by multiplying the unit selling price of each product by the number of units produced and sold (X1, X2, X3, X4). This approach ensures that the total revenue, which is the sum of the individual revenues from each product, is maximized.

the answer of the question is an option D i.e. Answer - 75X1 + 70X2 + 55X3 + 45X4

For the following problem, what would be the objective function that aims at maximizing the total revenue considering that X1, X2, X3, and X4 are the number of units produced and sold of Products 1, 2, 3, and 4, respectively? Manufacturing time (hr) per unit Machine Cost per hr (S) Product 1 Product ? Product 2 Product d Capacity (he)

For the following problem, what would be the objective function that aims at maximizing the total revenue considering that X1, X2, X3, and X4 are the number of units produced and sold of Products 1, 2, 3, and 4, respectively? Manufacturing time (hr) per unit Machine Cost per hr (S) Product 1 Product ? Product 2 Product d Capacity (he)

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Project analysis

Project analysis is the process of determining the aspects of a project in project management. This analysis helps in identifying whether the project is executing as expected and uses the specified budget. By conducting a project analysis, the current or future problems that occur during the project can be identified.

Question

### Objective Function for Maximizing Total Revenue

#### Problem Statement:
For the following problem, what would be the objective function that aims at maximizing the total revenue considering that X1, X2, X3, and X4 are the number of units produced and sold of Products 1, 2, 3, and 4, respectively?

#### Data Table:
The table below contains the cost per hour for different machines, the manufacturing time required for each product by each machine, and the machine capacities in hours.

**Manufacturing Time (hr) per unit**
| Machine | Cost per hr ($) | Product 1 | Product 2 | Product 3 | Product 4 | Capacity (hr) |
| --- | --- | --- | --- | --- | --- | --- |
| 1 | 10 | 2 | 3 | 4 | 2 | 500 |
| 2 | 5 | 2 | 1 | 1 | 1 | 380 |
| 3 | 4 | 7 | 3 | 2 | 1 | 450 |

**Unit Selling Price ($)**
| Product 1 | Product 2 | Product 3 | Product 4 |
| --- | --- | --- | --- |
| 75 | 70 | 55 | 45 |

#### Question:
What is the correct objective function to maximize the total revenue?

#### Multiple Choice Options:
- a. 12X1 + 8X2 + 7X3 + 5X4
- b. None of the answers
- c. 20X1 + 30X2 + 40X3 + 20X4
- d. 75X1 + 70X2 + 55X3 + 45X4

#### Answer:
The correct objective function is:
**d. 75X1 + 70X2 + 55X3 + 45X4**

This choice reflects the revenue generated by each product based on their unit selling price.

#### Explanation:
The objective function is constructed by multiplying the unit selling price of each product by the number of units produced and sold (X1, X2, X3, X4). This approach ensures that the total revenue, which is the sum of the individual revenues from each product, is maximized.

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