A manufacturer requires 15000 units of a part annually for assembly. Manufacturer can produce this at the rate of 100 per day. Set up cost for each production run is Rs. 24/- . to hold one unit of this part in inventory will cost Rs. 5/- per year. Determine the optimum manufacturing quantity and the optimum number of production run in any year.

Subordinates differ-in efficiency and tasks differ in their intrinsic difficulty. His estimate of time each man would take to perform each task is given in the matrix below :
TASKS SUBORDINATE 1 2 3 4
A
8
26
17
11
B
13
28
14
26
C
38
19
18
15
D
19
26
24
10
How should the tasks be allotted, one to a man, so as to minimize the total manhours

Solve the following LP problem through SIMPLEX method

Minimize Z = 2x₁ + 5x₂

Subject to x₁ + x₂ = 100

x₁ ≤ 40

x₂ ≥ 30

x₁, x₂ ≥ 0

What functions does inventory perform ?
State the two basic inventory decisions management must make in order to accomplish the functions of inventory just describe by you.

A repair and maintenance company is engaged in providing service to a particular brand of popular vehicle. It uses 8000 units of a moving parts per year as replacements of the old parts. Each part costs Rs. 250/-. The setup costs are estimated at Rs. 100 and the inventory carrying cost is the average of such inventory at 20% of the price. Supply of the part is at the rate of 80 per day. Calculate the following :
(i)Optimal order quantity
(ii)Optimal number of set ups,
(iii)Total variable costs based on optimal policy.
Assume 310 working days in a year

Dynamic programming

Distinguish between pure and mixed strategy for a game.