MTH601 Current FinalTerm Paper 29 August 2016

The cost of a new machine is Rs. 5000. The maintenance cost during the nth year is given by Mn = Rs. 500 (n – 1), where n = 1, 2, 3, ---. If the discount rate per year is 0.05, determine discount factor ( ) for each year.

Write the following constraints in standard form:

Describe the factors on which Dual of a Linear Programming problem depends?

If a company can produce an item at the rate of 2500 per month with no Shortage and the Demand for an item in a company is 15000 units / year. Further,
Setup Cost = Rs. 400 per order
Carrying Cost = Rs. 1 per item per month.
Then find the Optimum Manufacturing Quantity.

Write the standard form of the following linear programming problem,
Minimize Z = 2x1+3x2 +x3
Subject to
x1+4 x2+2x3 ≥8
3x1+2x2 ≥6
x1, x2, x3 ≥0

Give the simultaneous contrast of Dual when some features of Primal form of a Linear Programming problem are given as below;
The annual demand of an item is 1600 units per year while the cost of placing an order is Rs.5 and the holding cost is 10% per year. Then find optimal Costs of both phases such that 400 units and 404 units respectively. Further the Price breaks for both phases (discounts) are as follows:

Quantity Unit Cost
0 ≤ Q1 ≤ 800 Rs. 1.00
800 ≤ Q2 Rs. 0.98

A company centre has got four expert programmers. The centre needs four application programmes to be developed. The head of the computer centre, after studying carefully the programme’s to be developed, estimate the computer time in minutes required by the respective experts to develop the application programmes as follows.

Programmers A B C D
1 120 100 80 90
2 80 90 110 70
3 110 140 120 100
4 90 90 80 90

Optimize the solution.

The initial cost of an item is Rs. 1500 and maintenance or running cost for different years is given below.

Year 1 2 3 4
Running cost Rs. 200 400 500 700

What is the replacement policy to be adopted if the capital is worth 10% and no salvage value?
Maximize: z = 4x + 5y.
under the constraints;
4x + 3y ≤ 12.
2x – 3y ≤6
x + 2y ≤ 8
x,y≥0

A vendor has to supply 100 paper rims per day to different destinations. He finds that, when he starts the production, he can produce 300 rims per day. The cost of holding one in the warehouse is Rs. 2 per year and the setup cost of manufacturing cycle is Rs.30. How frequently should the manufacturing be made?