Explanation Given: Chemistry department decided to stock at least 800 small test tubes and 500 large test tubes. It wants to buy at least 1500 test tubes to avail the special price. Also, the number of small test tube must be at least twice of large test tube as it is broken twice often as large. Also, the cost of small test tube is 15 ¢ and cost of larger test tube is 12 ¢ . Formula used: Calculation: Assume y 1 be the number of small test tube purchased and y 2 be the number of large test tube purchased. So, minimize 15 y 1 + 12 y 2 to obtain minimum cost of purchase both of them. Since, department need at least 800 small test tube and 500 large test tube: y 1 ≥ 800 y 2 ≥ 500 Also, the department wants to buy at least 1500 test tubes. Therefore, y 1 + y 2 ≥ 1500 And the number of small test tube must be at least twice of large test tubes. Therefore, y 1 ≥ 2 y 2 y 1 − 2 y 2 ≥ 0 Hence, all the formed equations are: y 1 ≥ 800 y 2 ≥ 500 y 1 + y 2 ≥ 1500 y 1 − 2 y 2 ≥ 0 Now, write the above system linear inequalities as a system of linear equations. For this add slack or subtract surplus variables as required: y 1 − s 1 = 800 y 2 − s 2 = 500 y 1 + y 2 − s 4 = 1500 y 1 − 2 y 2 − s 3 = 0 Where, y 1 ≥ 0 , y 2 ≥ 0 , s 1 ≥ 0 , s 2 ≥ 0 , s 3 ≥ 0 and s 4 ≥ 0 . And, the equation to be minimized is: w = 15 y 1 + 12 y 2 Let z = − w , that implies: z = − 15 y 1 − 12 y 2 Now, form the initial simplex tableau from the formed equation: y 1 y 2 s 1 s 2 s 3 s 4 [ 1 0 − 1 0 0 0 800 0 1 0 − 1 0 0 500 1 1 0 0 − 1 0 1500 1 − 2 0 0 0 − 1 0 15 12 0 0 0 0 0 ] So, from above the basic solution is: y 1 = 0 , y 2 = 0 , s 1 = − 800 , s 2 − 500 , s 3 = − 1500 And s 4 = 0 …… (1) Here, as three variables are negative, the solution is not feasible. As, s 1 in equation (1) is negative. Therefore, take 1 as pivot in row 1 of column 1

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

11th Edition

ISBN: 9781323751671

Author: Lial

Publisher: PEARSON C

See similar textbooks

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

Videos

Question

Chapter 7.7, Problem 40E

To determine

To calculate: Number of each test tube to be purchased so as to minimize cost of purchase.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.7, Problem 39E

Chapter 7.7, Problem 41E

Students have asked these similar questions

How parents can assess children's learning at home and how the task can be differentiated. Must provide two examples of differentiation tasks. Mathematics in Practice Assignment 2

When ever one Point sets in X are closed a collection of functions which separates Points from closed set will separates Point. 18 (prod) is product topological space then xe A (xx, Tx) is homeomorphic to sub space of the Product space (TXA, prod). KeA The Bin Projection map 18: Tx XP is continuous and open but heed hot to be closed. Acale ctioneA} of continuos function ona topogical Space X se partes Points from closed sets inx iff the set (v) for KEA and Vopen set inx from a base for top on X-

Why are Bartleby experts giving only chatgpt answers?? Why are you wasting our Money and time ?

Chapter 7 Solutions

MATH W/APPLICAT.W/NOTES GDE +ACCESS CODE

Ch. 7.1 - Checkpoint 1 Graph the given...Ch. 7.1 - Prob. 2CP Ch. 7.1 - Prob. 3CP Ch. 7.1 - Prob. 4CP Ch. 7.1 - Prob. 5CP Ch. 7.1 - Checkpoint 6 Graph the feasible region of the...Ch. 7.1 - Prob. 7CP Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...Ch. 7.1 - Match the inequality with its graph, which is one...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.