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Operations Research

A company has three cement plants from which cement has to be transported to four distribution centres. With identical costs of production at the three plants, the only variable costs involved are transportation costs. The monthly demand at the four distribution centres and the distance from the plants to the distribution centres (in km) are given below: Distribution centres Plants Monthly production (tonnes) 500 1,000 150 800 10,000 200 700 500 100 12,000 600 400 100 900 8,000 Monthly demand (tonnes) 9,000 9,000 10,000 4,000 The transportation charges are ? 10 per tonne per km. Suggest optimal transportation schedule and indicate the total minimum transportation cost. Specially Structured Linear Programmes I: Transportation and Transhipment Problems • 295 If, for certain reasons, route from plant C to distribution centre X is closed down, will the transp- ortation schedule change? If so, suggest the new schedule and effect on total cost.

Operations Research

A tractor operator has only one tractor and he operates it on the job order from farmers. The requestors for the jobs arrive with Poisson distribution having interval time of 0.7 day. The average time to do a job is distributed exponentially with mean 0.5 day. Assuming that the tractor can take up the next job immediately on completion of the previous job, determine the following: i. Will a queue be formed? Explain ii. If queue is formed will it statistically stabilize? Explain your answer iii. What is the utilization factor of the tractor? iv. What is the idle time in daily duty of 7 hours? v. What is the mean number of job orders waiting? vi. What is the mean waiting time for job orders in the system? vii. What is the mean waiting time in the queue?

Operations Research

A firm makes items A and B and the total number of items it can make in a day is 24 It takes one hour to make an item of A and only half an hour to make an item of B. The maximum time available per day is 16 hours. The profit on an item of A is Rs. 300 and on one item of B is Rs.

Operations Research

Operations Research

Use Simplex method to

Maximize Ζ = 4_{x }+ 10_{x2}

Subject 2_{X}+_{X2} ≤ 50

2_{X} + 5_{X2} ≤ 100

2_{X} + 3_{X2 } ≤ 100

_{X, X2 } ≥ 0

Operations Research

The Eastern Iron and Steel Company makes nails, bolts, and washers from leftover steel and coats them with zinc. The company has 24 tons of steel and 30 tons of zinc available. The requirements for ingredients ( in tons per batch) and the profit for each product (in thousand dollars per batch) are given in the chart. The company wants to determine how many batches of each product should be produced to maximize profit.

Operations Research

For an objective function, Min Z = 10x + 20y; if the corner points are (0,18), (2,6), (4,2), (12,0); the optimal value of Z is

Operations Research

The Eastern Iron and Steel Company makes nails, bolts, and washers from leftover steel and coats them with zinc. The company has 24 tons of steel and 30 tons of zinc. The following linear pro- gramming model has been developed for determining the number of batches of nails (x1), bolts (x2), and washers (x3) to produce to maximize profit:

maximize Z = 6x1+2x2+12x3(profit,$1,000s) subject to

2x1+ 6x2 + 3x3 smaller than or equal to 30 (zinc, tons)

4X1+ x2+3x3 smaller than or equal to24(steel, tons)

x1, x2, x3 bigger than or equal to 0

Solve this model using the simplex method

Operations Research

The Cookie Monster Store at South Acres Mall makes three types of cookies—chocolate chip,

pecan chip, and pecan sandies. Three primary ingredients are chocolate chips, pecans, and sugar.

The store has 120 pounds of chocolate chips, 40 pounds of pecans, and 300 pounds of sugar. The

following linear programming model has been developed for determining the number of batches

of chocolate chip cookies pecan chip cookies and pecan sandies to make to maximize profit:

maximize Z = 10x1 + 12x2 + 7x3 (profit, $)

subject to:

x1 + 2x3 smaller than or equal to 40 (pecans, lb.)

10x1 + 5x2 smaller than or equal to 120 (chocolate chips, lb.)

20x1 + 15x2 + 10x3 smaller than or equal to 300(sugar, lb.)

x1, x2, x3 bigger than or equal to 0

Solve this model using the simplex method.

Operations Research

A baby products firm produces a strained baby food containing liver and milk, each of which con- tribute protein and iron to the baby food. Each jar of baby food must have 36 milligrams of protein and 50 milligrams of iron. The company has developed the following linear programming model to determine the number of ounces of liver (x1) and milk (x2) to include in each jar of baby food to meet the requirements for protein and iron at the minimum cost.

minimize Z = 0.05x1 + 0.10x2 (cost, $) subject to

6x1+ 2x2 > or equal to 36 (protein, mg)

5x1 + 5x2 >or equal to 50 (iron, mg)

X1, X2> or equal to 0

Solve this model using the simplex method.