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.
First, let's solve this step by step manually. This is a classical Economic Order Quantity (EOQ) / Production Inventory problem where we compare buying vs. manufacturing. --- Given data: * Annual demand: (D = 2500) units * Purchase cost: (C = ₹30) per unit * Ordering cost: (S = ₹15) per order * Holding cost: (H = ₹4) per unit per year If manufactured internally: * Cost saving: 20% of ₹30 → manufacturing cost per unit: (C_m = 30 \times 0.8 = ₹24) * Set-up cost: (S_m = ₹250) per production run * Production rate: (P = 4800) units/year * Holding cost: (H = ₹4) per unit per year --- ### Step 1: EOQ if purchased The EOQ formula for purchasing: [ EOQ = \sqrt{\frac{2DS}{H}} ____ ________ _____ _____ ___ ____ ______ ____ ________ _________.
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) Use simplex method to solve the following LPP:
Maximize:
Subject to the constraints:
and .
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 1x1/3 patients to 1/2 a patient?
| Activity | Time |
|---|---|
| 1 – 2 | 4 |
| 1 – 3 | 1 |
| 2 – 4 | 1 |
| 3 – 4 | 1 |
| 3 – 5 | 6 |
| 4 – 9 | 5 |
| 5 – 6 | 4 |
| 5 – 7 | 8 |
| 6 – 8 | 1 |
| 7 – 8 | 2 |
| 8 – 10 | 5 |
| 9 – 10 | 7 |
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?
| Job | Machine A | Machine B |
| J₁ | 1 | 5 |
| J₂ | 3 | 6 |
| J₃ | 8 | 3 |
| J₄ | 5 | 2 |
| J₅ | 6 | 2 |
| J₆ | 3 | 10 |
Obtain all the basic solutions to the following system of linear equations:
Which of the solutions are feasible? Justify.
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 |
Use two-phase method to solve the following LPP:
Maximize:
Subject to the constraints:
निम्नलिखित LPP को हल करने के लिए द्वि-विमीय विधि का प्रयोग कीजिए: का अधिकतमीकरण कीजिए
जबकि :