Search & Filtering
Critically examine Discovery’s use of game theory. Provide two examples of game theory as used by Discovery as a whole or any business units.
b) The Farmer decides to buy his bags of food A and food B from another store. This store sells a bag of food A for $9 and a bag of food B for $11. However, the farmer realised the new food bags are perishable. If the farmer does not use an entire bag, the food will spoil. The farmer must now use all of the contents of each bag. Use the linear programming process for this scenario to determine how many bags of food A and B the farmer now needs to meet the animals' minimum daily requirements for a minimum cost. Does the Farmer save any money but purchasing from another store?
The manager of a grocery store in the retirement community of Kapiri is interested in providing good service to the senior citizens who shop in his store. Presently, the store has a separate check-out counter for senior citizens. On average, 30 senior citizens per hour arrive at the counter according to a Poisson distribution and are served at an average rate of 35 customers per hour with exponential service times. Find the following;
(a) Utilization of the checkout clerk
(b) Number of customers in a system
(c) Number of customers in line
(d) Time spent in the system
(e) Waiting time in line
The manager of Kapiri grocery wants to answer the following question:
(1) What service rate would be required to have customers average only eight minutes in
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.
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?
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.
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?
Use Simplex method to
Maximize Ζ = 4x + 10x2
Subject 2X+X2 ≤ 50
2X + 5X2 ≤ 100
2X + 3X2 ≤ 100
X, X2 ≥ 0
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.
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
