Introductio1
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Apeejay Institute of Technology *
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Course
MISC
Subject
Health Science
Date
Nov 24, 2024
Type
docx
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2
Uploaded by AmbassadorComputer10264
Introduction:
Winding Brook Farms is in the business of producing animal feed for its livestock. To
optimize costs and ensure that the animals receive the necessary nutrients, the farm is
considering a mix of two types of ingredients: Ingredient A and Ingredient B. These
ingredients have different costs and nutrient compositions. The goal is to determine the
optimal combination of these ingredients to create a low-cost feed mix while meeting the
daily minimum requirements for proteins, minerals, and vitamins. This problem can be
addressed using linear programming, a mathematical approach that helps find the best
solution to minimize costs while satisfying constraints.
Problem Breakdown:
Here's a breakdown of the problem:
1. Ingredients and Costs:
- Ingredient A costs $9.00 and contains 40 units of proteins, 20 units of minerals, and 10 units
of vitamins.
- Ingredient B costs $15.75 and contains 30 units of proteins, 20 units of minerals, and 30
units of vitamins.
2. Daily Minimum Requirements:
- The farm has daily minimum requirements of 140 units of proteins, 85 units of minerals,
and 60 units of vitamins for its animal feed.
3. Objective:
- Determine the lowest possible cost for creating the feed mix using Ingredient A and
Ingredient B.
4. Constraints:
- The constraints include the minimum nutrient requirements for proteins, minerals, and
vitamins, which must be met by the feed mix.
5. Part (a):
- Calculate the optimal amounts of Ingredient A and Ingredient B that should be part of the
mix to minimize costs while meeting the nutrient constraints.
6. Part (b):
- Calculate the overall cost of the optimal feed mix obtained in part (a).
7. Part (c):
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