Explanation Consider a problem with mix production for a business. A company produces nuts and bolts for industrial machinery. It includes working on machine A and takes 3 hours for machine B to produce a package of nuts, and on the other hand, it takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. The company owner earns a profit of $ 2.50 per package of nuts and $ 1.0 per package of bolts. Then the number of packages of each should produce each day, to maximize his profit, if the machines are operated at most 12 hours in a day. Step 1: Transform the given information in the tabular form. Machine Time required to produce products Max machine hours available Nuts Bolts A 1 3 12 B 3 1 12 Profit in $ 2.50 1.0 Step 2: Assume the variables such that the company produce x packages of nuts and y packages of bolts per day. Step 3: Obtain the objective function for maximizing the profit earned as shown below: P = 2.5 x + y Step 4: Create the constraints according to the restrictions applied on the problem. For machine A it takes one hour to produce one package of nuts and 3 hours to produce the one package of bolts then to produce x packages of nuts and y packages of bolts machine A operated for 12 hours . x + 3 y ≤ 12 For machine B it takes 3 hours to produce one package of nuts and one hour to produce the one package of bolts then to produce x packages of nuts and y packages of bolts machine B operated for 12 hours . 3 x + y ≤ 12 and x , y ≥ 0 Solve this problem by plotting the graph by following the below mentioned steps: Step 1: To plot a graph convert the inequality constraint in equality equation. x + 3 y = 12 3 x + y = 12 Step 2: Find the coordinates of the equations by substituting the corner point ( x , 0 ) and ( 0 , y ) . For equation x + 3 y = 12 , substitute the corner point ( x , 0 ) and ( 0 , y ) . When the corner point is ( x , 0 ) , then the value of x can be computed as shown below: x + 3 y = 12 x + 3 × 0 = 12 x = 12 So, the corner point is ( 12 , 0 ) . When the corner point is ( 0 , y ) , then the value of y can be computed as shown below: x + 3 y = 12 0 + 3 y = 12 3 y = 12 y = 4 So, the corner point is ( 0 , 4 ) . Hence, the corner points for x + 3 y = 12 are ( 12 , 0 ) and ( 0 , 4 ) . For equation 3 x + y = 12 , substitute the corner point ( x , 0 ) and ( 0 , y ) . When the corner point is ( x , 0 ) then the value of x can be computed as shown below: 3 x + y = 12 3 x + 0 = 12 3 x = 12 x = 4 So, the corner point is ( 4 , 0 ) . When the corner point is ( 0 , y ) , then the value of y can be computed as shown below: 3 x + y = 12 3 × 0 + y = 12 y = 12 So, the corner point is ( 0 , 12 ) . Hence, the corner points for the equation 3 x + y = 12 are ( 4 , 0 ) and ( 0 , 12 )

5th Edition

ISBN: 9780321837240

Author: Robert F. Blitzer

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 8.6, Problem 36E

To determine

That how the production policy decisions made. Also, explain other methods in conjunction with linear programming if any. The academic background of the executive. Also, present the report emphasizing the role of linear programming for the business.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.6, Problem 35E

Chapter 8.6, Problem 37E

Students have asked these similar questions

Graph without using the calculator y-1 = | x+4 |

9:43 AS く Akbar © Printed in the United States 15) Scale: 1 cmal unit on both axes .ill 64% The graph above shows a straight line QT intersecting the y-axis at T. i State the co-ordinates of T. ii Calculate the gradient of QT 16) iii Determine the equation of QT. A (-1, 9) ||| i L Г (5 marks)

Pls help.

Chapter 8 Solutions

Algebra and Trigonometry

Knowledge Booster

$Algebra$

Learn more about

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