Answered: A botanist can purchase plant food of…

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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Question

A botanist can purchase plant food of four different types, I, II, III, and IV. Each food comes in the same size bag, and the following table summarizes the number of grams of each of three nutrients that each bag contains.

	Food (grams)
	I	II	III	IV
Nutrient A	5	5	10	5
Nutrient B	10	5	30	10
Nutrient C	5	15	10	25

The botanist wants to use a food that has these nutrients in a different proportion and determines that he will need a total of 8,000 g of A, 18,000 g of B, and 14,000 g of C. Let

x = Type I bags,

y = Type II bags,

z = Type III bags,

and

w = Type IV bags.

Write an equation for the total number of grams of Nutrient A in terms of x, y, z, and w.

Write an equation for the total number of grams of Nutrient B in terms of x, y, z, and w.

Write an equation for the total number of grams of Nutrient C in terms of x, y, z, and w.

Find the number of bags of each type of food that should be ordered. (If there are infinitely many solutions, express your answers in terms of w as in Example 3.)

(x, y, z, w) =

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