Explanation Given Information: The following table is based on four bodybuilding supplements, Creatine (grams) L-Glutamine (grams) BCAAs (grams) Cost ($) Xtend (SciVation) 0 2.5 7 1 Gainz (MP Hardcore) 2 3 6 1.10 Strongevity (Bill Phillips) 2.5 1 0 1.20 Muscle Physique (EAS) 2 2 0 1.00 Formula used: The steps for Linear Programming problems: 1. First, draw a rectangle that is big enough such that it encompasses all the corner points that are present. 2. Then, mark the outside of the rectangle in order to highlight a new bounded feasible region after which, discern the new corner points. 3. Use the bounded feasible region to obtain the optimal solutions. 4. If the optimal solution occurs at the one of the corner points, then LP problem has that corner point as optimal solution otherwise it has no optimal solution. Calculation: Consider the number of serving of Xtend to be x. Consider the number of serving of Gainz to be y. Consider the first constraint equation. 2 y = 4 y = 4 2 y = 2 There is straight line passing through ( 0 , 2 ) . Test the second inequality by ( 0 , 0 ) test coordinates. 2 y ≥ 4 2 ⋅ 0 ≥ ? 4 0 ≥ 4 The inequality is not satisfied. A case in which the test point does not satisfy the inequality, the set of solutions is the line plus the complete region on the other side of the line i.e. away from the test coordinate ( 0 , 0 ) . Consider the second constraint equation. 2.5 x + 3 y = 36 Isolate the variable y , by subtracting 2.5 x from both sides, 2.5 x − 2.5 x + 3 y = 36 − 2.5 x 3 y = 36 − 2.5 x y = ( 36 − 2.5 x ) 3 y = 12 − 2.5 x 3 To plot the graph of the function, find the ordered pairs of the second constraint equation by substituting different values of x . For x = 0 , substitute 0 for x , y = 12 − 2.5 3 ⋅ 0 = 12 − 0 = 12 For x = 6 , substitute 6 for x , y = 12 − 2.5 3 ⋅ 6 = 12 − 2.5 ⋅ 2 = 12 − 5 = 7 For x = 12, substitute 12 for x, y = 12 − 2.5 3 ⋅ 12 = 12 − 2.5 ⋅ 4 = 12 − 10 = 2 Construct a table for the ordered pairs of second constraint equation, x 0 6 12 y 12 7 0 Test the second inequality by ( 0 , 0 ) test coordinates. 2.5 x + 3 y ≥ 36 2.5 ⋅ 0 + 3 ⋅ 0 ≥ ? 36 0 + 0 ≥ ? 36 0 ≥ 36 The inequality is not satisfied. A case in which case the test point does not satisfy the inequality, the set of solutions is the line plus the complete region on the other side of the line i.e. away from the test coordinate ( 0 , 0 ) . Consider the third constraint equation, 7 x + 6 y = 84 Isolate the variable y , by subtracting 7 x from both sides, 7 x − 7 x + 6 y = 84 − 7 x 6 y = 84 − 7 x y = ( 84 − 7 x ) 6 y = 14 − 7 6 ⋅ x To plot the graph of the function, find the ordered pairs of the third constraint equation by substituting different values of x . For x = 0 , substitute 0 for x , y = 14 − 7 6 ⋅ 0 = 14 − 0 = 14 For x = 6 , substitute 6 for x , y = 14 − 7 6 ⋅ 6 = 14 − 7 ⋅ 1 = 14 − 7 = 7 For x = 12, substitute 12 for x, y = 14 − 7 6 ⋅ 12 = 14 − 7 ⋅ 2 = 14 − 14 = 0 Construct a table for the ordered pairs of third constraint equation, x 0 6 12 y 14 7 0 Test the third inequality by ( 0 , 0 ) test coordinates

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 6.2, Problem 33E

To determine

To calculate: The servings of Xtend and Gainz that you should combine to obtain a week’s supply that meets someone’s specifications at the least cost. The personal trainer of someone’s friend suggests that the supplement he take should have at least 4 grams of creatine, 36 grams of L-glutamine, and 84 grams of BCAAs each week. The person thinks to combine Xtend and Gainz for the required nutrients.

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Chapter 6.2, Problem 32E

Chapter 6.2, Problem 34E

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Finite Mathematics and Applied Calculus (MindTap Course List)

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Solution Summary: The author explains how to calculate the servings of Xtend and Gainz to obtain a week's supply at the least cost.

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