The time taken (in hours) by five different machines for completing five different jobs is given below:
Find the optimal assignment.
To solve the assignment problem, we need to find the optimal assignment of jobs to machines such that the total time taken is minimized. This is typically done using the Hungarian Algorithm, which is an efficient method for solving such problems. ### Step 1: Understand the Problem We have a cost matrix where each element represents the time taken by a machine to complete a job. The goal is to assign each job to a unique machine such that the total time is minimized. ### Step 2: Apply the Hungarian Algorithm The Hungarian Algorithm involves the following steps: 1. Subtract the minimum value of each row from all elements of that __________ _____ ___ __________ ________ _______ __________ ______ _______ ________ __________ _____.
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Which of the following statements are true? Give reasons for your answers.
i) If an item is ordered frequently, then the risk of running out of stock is least.
ii) In deterministic queuing model, arrival rate must not exceed the service rate.
iii) The critical path of a project network represents the minimum time needed to complete the project.
iv) A necessary and sufficient condition for a basic feasible solution for a minimization LPP to be optimum is that all Zj - Cj 20.
v) If dual has an unbounded solution, primal has a feasible solution.
पाँच विभिन्न मशीनों द्वारा पाँच भिन्न-भिन्न कार्यों को पूरा करने में लगा समय (घंटों में) नीचे दिया गया है :
Use two-phase method to solve the following LPP:
Maximize:
z = 3x1 + 2x2
Subject to the constraints:
A firm produces there product A, B and C. It uses two types of raw materials I and II of which 5000 and 7500 units respectively are available. The raw material requirements per unit of the products are given below:
The minimum demand of the three products is 600, 650 and 500 units respectively. Assuming the profits per unit of A, B and C as ₹50, ₹50 and 280 respectively. Formulate the problem as LPP model in order to determine the number of units of each product which will maximize the profit.
एक आपातकालीन क्लीनिक की आवश्यकता औसतन 96 रोगियों को प्रति 24 घंटे दैनिक होती है। औसतन एक रोगी को सक्रिय ध्यान के 10 मिनट आवश्यक हैं। मान लीजिए कि यह सुविधा एक समय में एक ही रोगी के लिए उपलब्ध है। मान लीजिए कि 10 मिनट की औसतन सेवा के लिए एक रोगी पर₹ 100 की लागत आती है, और इससे एक भी मिनट कम होने पर ₹ 10 प्रति रोगी लागत होती है। क्लीनिक को बजट में कितनी मात्रा रखनी चाहिए कि पंक्ति का औसतन आकार रोगी से 1 2
रोगी हो जाए?
एक फर्म तीन उत्पाद A, B और C बनाती है। यह दो प्रकार I और II का कच्चा माल प्रयोग करती है जिसकी क्रमशः 5000 और 7500 इकाइयाँ उपलब्ध हैं। प्रत्येक उत्पाद की इकाइयों के लिए आवश्यक कच्चा माल नीचे दिया गया है:
| कच्चा माल | उत्पाद की प्रति इकाई आवश्यकता | ||
| A | B | C | |
| I | 3 | 4 | 5 |
| II | 5 | 3 | 5 |
On an average 96 patients per 24-hour a day require the services of an emergency clinic. Also on an average, a patient requires 10 minutes of active attention. Assume that the facility can handle only one emergency at a time. Suppose that it costs the clinic ₹ 100 per patient treated to obtain an average servicing time of 10 minutes, and that each minute of decrease in this average time would cost ₹ 10 per patient treated. How much would have to budgetted by the clinic to decrease the average size of the queue from patients to
a patient?