An ambitious Texas A&M student is training to become a competitive weightlifter in addition to being a math major. Her exercise program has three components: upper body strength, lower body strength, and endurance training. She needs to do at least 7 hours of upper body strength, 4 hours of lower body strength, and 9 hours of endurance training each week. There are three gym programs in College Station she can use. The exercise components of the three gym programs are summarized in the table below. Minutes of upper body strength Minutes of lower body strength Minutes of endurance training Cost Gym Program 1 22 34 32 35 Gym Program 2 34 37 26 45 Gym Program 3 23 37 39 35 The student wants to determine the number of sessions at each gym she should attend in order to achieve her goals in the cheapest way possible. (a) Identify and clearly define the variables needed to solve the linear programming problem. x= y= z= C= (b) Find the objective function. Select whether it's maximizing or minimizing in the first answer blank and enter your equation in the second answer blank. (Hint: Your equation must be written in the form C = , where the variable you are maximizing or minimizing is on the left side of the equal sign.) (c) The objective function is subject to constraints. Determine the constraints below. (Hint: Write the constraints line by line. Separate the non-negativity constraints with commas.) upper body strength constraint in minutes lower body strength constraint in minutes endurance training constraint in minutes non-negativity constraints

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

An ambitious Texas A&M student is training to become a competitive weightlifter in addition to being a math major.

Her exercise program has three components: upper body strength, lower body strength, and endurance training. She needs to do at least 7 hours of upper body strength, 4 hours of lower body strength, and 9 hours of endurance training each week.

There are three gym programs in College Station she can use. The exercise components of the three gym programs are summarized in the table below.

	Minutes of upper body strength	Minutes of lower body strength	Minutes of endurance training	Cost
Gym Program 1	22	34	32	35
Gym Program 2	34	37	26	45
Gym Program 3	23	37	39	35

The student wants to determine the number of sessions at each gym she should attend in order to achieve her goals in the cheapest way possible.

(a)

Identify and clearly define the variables needed to solve the linear programming problem.

x= y= z= C=

(b)

Find the objective function. Select whether it's maximizing or minimizing in the first answer blank and enter your equation in the second answer blank. (Hint: Your equation must be written in the form C = , where the variable you are maximizing or minimizing is on the left side of the equal sign.)

(c)

The objective function is subject to constraints. Determine the constraints below. (Hint: Write the constraints line by line. Separate the non-negativity constraints with commas.)

upper body strength constraint in minutes

lower body strength constraint in minutes

endurance training constraint in minutes

non-negativity constraints

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