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A cattle-breeder has two types of cattle-fodder. The first type contains 60 units of carbohydrates and 20 units of proteins per kilogram. The second one contains 40 units of carbohydrates and 30 units of proteins per kilogram. The stock of cattle needs (at least) 20 000 units of carbohydrates and 12 000 units of proteins per day. The price per kilogram of the fodder of the first type is €1.5 and the second type costs €1 per kilogram. There is a contract with the supplying firm that the cattle-breeder will buy at least 50 kilogram a day of the fodder of the first type. (a) Determine the minimum value for the total daily cost of the fodder and find out how much of each type the cattle-breeder has to buy to attain this minimum value for the cost. (b) Would it be cheaper if there was no agreement to buy at least 50 kilogram a day of the first type of fodder? Notes

A cattle-breeder has two types of cattle-fodder. The first type contains 60 units of carbohydrates and 20 units of proteins per kilogram. The second one contains 40 units of carbohydrates and 30 units of proteins per kilogram. The stock of cattle needs (at least) 20 000 units of carbohydrates and 12 000 units of proteins per day. The price per kilogram of the fodder of the first type is €1.5 and the second type costs €1 per kilogram. There is a contract with the supplying firm that the cattle-breeder will buy at least 50 kilogram a day of the fodder of the first type. (a) Determine the minimum value for the total daily cost of the fodder and find out how much of each type the cattle-breeder has to buy to attain this minimum value for the cost. (b) Would it be cheaper if there was no agreement to buy at least 50 kilogram a day of the first type of fodder? Notes

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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35. A cattle-breeder has two types of cattle-fodder. The first type contains 60 units of carbohydrates and 20 units of proteins per kilogram. The second one contains 40 units of carbohydrates and 30 units of proteins per kilogram. The stock of cattle needs (at least) 20 000 units of carbohydrates and 12 000 units of proteins per day. The price per kilogram of the fodder of the first type is €1.5 and the second type costs €1 per kilogram. There is a contract with the supplying firm that the cattle-breeder will buy at least 50 kilogram a day of the fodder of the first type. (a) Determine the minimum value for the total daily cost of the fodder and find out how much of each type the cattle-breeder has to buy to attain this minimum value for the cost. (b) Would it be cheaper if there was no agreement to buy at least 50 kilogram a day of the first type of fodder? Notes
Transcribed Image Text:35. A cattle-breeder has two types of cattle-fodder. The first type contains 60 units of carbohydrates and 20 units of proteins per kilogram. The second one contains 40 units of carbohydrates and 30 units of proteins per kilogram. The stock of cattle needs (at least) 20 000 units of carbohydrates and 12 000 units of proteins per day. The price per kilogram of the fodder of the first type is €1.5 and the second type costs €1 per kilogram. There is a contract with the supplying firm that the cattle-breeder will buy at least 50 kilogram a day of the fodder of the first type. (a) Determine the minimum value for the total daily cost of the fodder and find out how much of each type the cattle-breeder has to buy to attain this minimum value for the cost. (b) Would it be cheaper if there was no agreement to buy at least 50 kilogram a day of the first type of fodder? Notes
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