A small firm makes three products, which all follow the same three-step process, which consists of...

80.2K

Verified Solution

Question

General Management

A small firm makes three products, which all follow the samethree-step process, which consists of milling, inspection, anddrilling. Product A requires 6 minutes of milling, 5 minutes ofinspection, and 4 minutes of drilling; product B requires 2.5minutes of milling, 2 minutes of inspection, and 2 minutes ofdrilling; and product C requires 5 minutes of milling, 4 minutes ofinspection, and 8 minutes of drilling. The department has 20 hoursavailable during the next period for milling, 15 hours forinspection, and 24 hours for drilling. Product A contributes $6.00per unit to profit, product B contributes $4.00 per unit, andproduct C contributes $10.00 per unit. The following is the outputmaximizing profits for the next period: PROBLEM TITLE: LINEARPROGRAMMING PROBLEM IS A MAX WITH 3 VARIABLES AND 3 CONSTRAINTS.Row X1 X2 X3 Cost 6.00 4.00 10.00 1 6.00 2.50 5.00 1,200.00 2 5.002.00 4.00 900.00 3 4.00 2.00 8.00 1,440.00 NUMBER OF ITERATIONS: 2OPTIMAL SOLUTION: OBJECTIVE FUNCTION VALUE = 2,070 DECISIONVARIABLE SECTION: Variable Status Value Reduced Cost X1 Non-basic 03.5 X2 Basic 180 0 X3 Basic 135 0 SLACK VARIABLES SECTION: SlackStatus Value Shadow Price X4 Basic 75 0 X5 Non-basic 0 1.5 X6Non-basic 0 .5

What would the objective function value be if 3 more units ofeach X4, X5, and X6 were added assuming they are within the rangeof optimality?

Answer & Explanation Solved by verified expert
4.5 Ratings (924 Votes)
The status of the constraints or variables X4 X5 and X6 in the optimal solution is as follows Variables Slack status Value Shadow Price X4 Basic 75 0 X5 Nonbasic 0 15 X6 Nonbasic 0 05 The variable X4 is still basic variable the amount of 75 hours is remaining after    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students