To find: the possible number of batches of soap and shampoo in order to maximize the number of batches; if not possible state whether the problem is infeasible, unbounded or has alternate optimal solutions.
Answer to Problem 20E
Soap batch: 0
Shampoo batch: 8
Explanation of Solution
Given information:
Let the number of soap and shampoo be
Amount of lye = 48 ounce
Amount of coconut oil = 76 ounce
Minimum lye use for
Maximum coconut oil use for
Minimum lye use for
Maximum coconut oil use for
Calculation:
Let
The inequalities derived from the given information are as follows:
Use a graphing calculator to plot the inequalities as shown below.
The vertices are
Thus, the possible number of batches of soap and shampoo in order to maximize the number of batchesis 0 and 8 respectively.
Chapter 2 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Additional Math Textbook Solutions
Precalculus (10th Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (2nd Edition)
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