निम्नलिखित LPP को हल करने के लिए एकधा विधि का प्रयोग कीजिए :
z = 2x1 - x2 + x3 का अधिकतमीकरण कीजिए
जबकि :
निम्नलिखित LPP को ग्राफीय विधि से हल कीजिए :
z = 2x1 + 3x2 का अधिकतमीकरण कीजिए जबकि :
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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 |
तीनों उत्पादों की न्यूनतम माँग क्रमशः 600, 650 और 500 इकाइयाँ है। मान लीजिए कि A, B और C की प्रत्येक इकाई पर लाभ क्रमशः ₹ 50, ₹50 और ₹80 है। लाभ का अधिकतमीकरण करने वाली LPP सूत्रित कीजिए।
See Answer →निम्नलिखित में से कौन-से कथन सत्य हैं और कौन-से असत्य हैं?
अपने उत्तर के पक्ष में एक संक्षिप्त उपपत्ति या प्रति-उदाहरण दीजिए:
i) यदि एक उत्पाद बार-बार ऑर्डर किया जाता है, तो स्टॉक की पुनरावृत्ति लागत का जोखिम कम i होता है।
ii) एक पंक्ति निदर्श के हल के लिए, आगमन दर, सेवा दर से अधिक नहीं होनी चाहिए।
iii) एक परियोजना नेटवर्क का क्रांतिक पथ उस परियोजना को पूरा करने में लगे न्यूनतम काल को दर्शाता है।
iv) एक अधिकतमीकरण LPP के आधारी सुसंगत हल के लिए आवश्यक और अनिवार्य प्रतिबंध है कि सभी Zj - Cj 20.
v) यदि द्वैती अपरिबद्ध है, तो आद्य का सुसंगत हल होता है।
See Answer →
A sales manager wishes to assign four sales territories to four salespersons. The salespersons differ in their ability and skills and consequently the sales expected in each territory are different. The estimates of sales per month for each sales-person in different territories are given below:
Find the optimal assignment of the four salespersons to the four different territories and the maximum monthly sales.
See Answer →Obtain all the basic solutions to the following system of linear equations:
Which of the solutions are feasible? Justify.
See Answer →At present a company is purchasing an item ‘x’ from outside suppliers. The assumption of unit is 10000 units/year. The cost of the item is ₹ 5 per unit and the ordering cost is estimated to be ₹ 100 per order. The cost of carrying inventory is 25%. If the consumption rate is uniform, determine the economic order quantity.
See Answer →Use branch and bound method to solve the following LPP:
Minimize:
Z + 4x1 + 3x2
Subject to the constraints:
x1,x2 ≥ and are integers.
See Answer →A road transport company has one reservation clerk on duty at a time. He handles information of bus schedules and make reservations. Consumers arrive at a rate of 8 per hour and the clerk can service 12 customers on an average per hour.
i) What is the average number of customers waiting for the service of the clerk?
ii) What is the average time a customer has to wait before getting service?
See Answer →A project schedule has the following characterizing:
i) Construct PERT network.
ii) Find the critical path.
See Answer →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?
A manufacturing company needs 2500 units of a particular item every year. The company buys it at the rate of ₹ 30 per unit. The order processing cost for this item is estimated at ₹ 15 and the cost of carrying a item in stock comes to about ₹ 4 per year. The company can manufacture this item internally. In that case it saves 20% of the price of the product. However, it estimates a set-up cost of ₹ 250 per production run. The annual production rate would be 4800 units. However, the inventory holding costs remain unchanged.
i) Determine the EOQ and the optimal number of orders placed in a year.
ii) Determine the optimum production lot size and the average duration of the production run.
See Answer →The time taken (in hours) by five different machines for completing five different jobs is given below:
Find the optimal assignment.
See Answer →In a factory, there are six jobs to perform each of which should go through two machines A and B in the order A B. The processing timings (in hours) for the jobs are given here. You are required to determine the sequence for performing the jobs that would minimize the total elapsed time T, what is the value of T?
Given x13 = 50units, x14 = 20 units, x21 = 55units, x31 = 30units, x2 = 35units and x34 = 25 units. Is it an optimal solution to the transportation problem:
Use dual simplex method to solve the following LPP:
Minimize:
z = 3x1 + x2
Subject to the constraints:
Use two-phase method to solve the following LPP:
Maximize:
z = 3x1 + 2x2
Subject to the constraints:
Use simplex method to solve the following LPP:
Maximize:
z = 2x1 - x2 + x3
Subject to the constraints:
x1 x2, ≥ 0 and x is unrestricted.
See Answer →Use the graphical method to solve the following LPP:
Maximize:
z = 2x1 + 3x2
Subject to the constraints:
