Use two-phase method to solve the following LPP:
Maximize:
Subject to the constraints:
Maximize ( z = 3x_1 + 2x_2 ) Subject to: ( 2x_1 + x_2 \le 2 ) ( 3x_1 + 4x_2 \ge 12 ) ( x_1, x_2 \ge 0 ) Step 1: Convert constraints to standard form with slack, surplus, and artificial variables. 1. ( 2x_1 + x_2 + s_1 = 2, \ s_1 \ge 0 ) (slack for ≤) 2. ( 3x_1 + 4x_2 - s_2 + A_1 = 12, \ s_2 \ge 0, A_1 \ge 0 ) (surplus and artificial for ≥) Step 2: Phase 1 – Minimize ( W = A_1 ) Initial basic variables: ( s_1 = 2 ), ( A_1 = 12 ) Phase 1 tableau (variables: ( x_1, x_2, s_1, s_2, A_1 )): | BV | (x_1) | ___ ___ __________ ________ ______ ___ ____ _______ _________.
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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?
The time taken (in hours) by five different machines for completing five different jobs is given below:
Find the optimal assignment.
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 .
v) If dual has an unbounded solution, primal has a feasible solution.
Use dual simplex method to solve the following LPP:
Minimize:
Subject to the constraints:
निम्नलिखित LPP को हल करने के लिए एकधा विधि का प्रयोग कीजिए : का अधिकतमीकरण कीजिए
जबकि :
तथा ।
ख) निम्नलिखित LPP की द्वैती लिखिए: का न्यूनतमीकरण कीजिए
जबकि : और x3 अप्रतिबंधित है।
) Use simplex method to solve the following LPP:
Maximize:
Subject to the constraints:
and .
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.