A department has five employees with five jobs to be performed. The time (in hours) each man will take to perform each job is given in the effectiveness matrix:

The annual sales revenue (in lakhs of Rs) of a product as a function of sales force (number of salesmen) and annual adverting expenditure (in Thousands of Rs) for the past 10 years are summarised in following table:

For the following Auto regressive model

X_t = 0.7X _{t -1} - 0.4 X_{t -2} + a t

i) Verify whether the series is Stationary

ii) Obtain p_k : k = 1, 2 ,3, 4 and 5

iii) Plot the Correlogram.

The production department for a company requires 3600 kg of raw material for manufacturing a particular item per year. It has been estimated that the cost of placing an order is Rs 36 and the cost of carrying inventory is 25 percent of the investment in the inventories. The price is Rs10 per kg. The purchase manager wishes to determine an ordering policy for raw material.

A company makes two kinds of leather belts. Belt A is a high quality belt and Belt B is of lower quality. The respective profits are Rs 4 and Rs 3 per belt. The production of each of type A requires twice as much time as a belt of type B, and if all belts were of type B, the company could make 1000 per day. The supply of leather is sufficient for only 800 belts per day (Both A and B combined). Belt A requires a fancy buckle and only 400 per day are available. There are only 700 buckles a day available for Belt B. What should be the daily production of each type of belt? Formulate this problem as an LP Model and solve it using Simplex Method.

A company has factories at F₁ , F₂ and F₃ which supply to Ware houses at W₁ , W₂ and W₃ .Weekly factory capacities are 200, 160 and 90 units, respectively. Weekly warehouse requirements are 180, 120 and 150 units, respectively. Unit shipping costs (in Rs) are as follows:

The demand (in thousands of units) of refrigerators manufactured by a company are    summarised in the following table: