Solve the following exercise using jupyter notebook for Python, to find the objective function, variables, constraint matrix and print the graph with the optimal solution. Use linear programming methods to solve this problem. Represent the constraints and the objective function mathematically in code. Use Python and the SciPy and Matplotlib libraries to solve the problem and visualize the optimal solution on a graph. Clearly state the optimal solution and any assumptions made while solving the problem. A farm specializes in the production of a special cattle feed, which is a mixture of corn and soybeans. The nutritional composition of these ingredients and their costs are as follows: - Corn contains 0.09 g of protein and 0.02 g of fiber per gram, with a cost of.$0.30 per gram.- Soybeans contain 0.60 g of protein and 0.06 g of fiber per gram, at a cost of $0.90 per gram.0.90 per gram. The dietary needs of the specialty food require a minimum of 30% protein and a maximum of 5% fiber. The farm wishes to determine the optimum ratios of corn and soybeans to produce a feed with minimal costs while maintaining nutritional constraints and ensuring that a minimum of 800 grams of feed is used daily. Restrictions 1. The total amount of feed should be at least 800 grams per day.2. The feed should contain at least 30% protein and no more than 5% fiber. ObjectiveMinimize the total daily cost of the feed mix. Questions1. How many grams of corn and soybeans should be used to minimize the daily cost?2. What is the minimum daily cost of the food mix?

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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Question

Solve the following exercise using jupyter notebook for Python, to find the objective function, variables, constraint matrix and print the graph with the optimal solution. Use linear programming methods to solve this problem. Represent the constraints and the objective function mathematically in code. Use Python and the SciPy and Matplotlib libraries to solve the problem and visualize the optimal solution on a graph. Clearly state the optimal solution and any assumptions made while solving the problem.

A farm specializes in the production of a special cattle feed, which is a mixture of corn and soybeans. The nutritional composition of these ingredients and their costs are as follows:

- Corn contains 0.09 g of protein and 0.02 g of fiber per gram, with a cost of.
$0.30 per gram.
- Soybeans contain 0.60 g of protein and 0.06 g of fiber per gram, at a cost of $0.90 per gram.
0.90 per gram.

The dietary needs of the specialty food require a minimum of 30% protein and a maximum of 5% fiber. The farm wishes to determine the optimum ratios of corn and soybeans to produce a feed with minimal costs while maintaining nutritional constraints and ensuring that a minimum of 800 grams of feed is used daily.

Restrictions

1. The total amount of feed should be at least 800 grams per day.
2. The feed should contain at least 30% protein and no more than 5% fiber.

Objective
Minimize the total daily cost of the feed mix.

Questions
1. How many grams of corn and soybeans should be used to minimize the daily cost?
2. What is the minimum daily cost of the food mix?

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