Find a starting feasible solution of the following transportation problem using: North West corner Least cost rule Least cost value in the column Penalty Method
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- Find the maximum and minimum values of the given objective function on the indicated feasible region. P=140x+3y {x0,y02x+y202x+4y5x+2y18}Consider the transportation problem given below. Destinations Source 1 2 3 Supplies 1 9 6 4 5 2 4 10 2 6 3 15 7 10 5 Demands 9 3 4 16 Construct the NW corner solution Compute the total cost of the NW corner solution Using the stepping stone method, find the min-cost solution.A distribution company is considering two locations for the construction of a new automated warehouse: Chicago and Dallas. Two types of automation are also being considered: bar coding and RF/ID (radio-frequency identification). The annual operating costs for each type of automation at the two locations are: Bar Coding RF/ID Location Fixed Cost Variable Cost per 1,000 units Fixed Cost Variable Cost per 1,000 units Chicago $1,800,000 $12.30 $2,700,000 $9.70 Dallas 1,500,000 13.10 2,300,000 9.40 For what range of annual product volume handled would each location and type of automation be preferred?
- A company has factories at F1, F2 and F3 which supply to warehouses at W1, W2 and W3. Weekly factory capacities are 200, 160 and 90 units, respectively. Weekly warehouse requiremnet are 180, 120 and 150 units, respectively. Unit shipping costs (in rupess) are as follows: W1 W2 W3 Supply F1 16 20 12 200 F2 14 8 18 160 F3 26 24 16 90 Demand 180 120 150 450 Determine the optimal distribution for this company to minimize total shipping cost.The accountant of Royal Products provided the following information for purposes of determining the optimal product mix: Product King (K) Product Queen (Q) Marginal income per unit R30 R36Machine hours required per unit 6 6Marginal income per machine hour R5 R6Ranking in terms of machine hours 2nd 1stLabour hours required per unit 3 6Marginal income per labour hour R10 R6Ranking in terms of labour hours 1st 2ndAnnual demand for product in units 12 000 15 000Labour hours available per annum 65 000 Machine hours available per annum 82 000 Required: Determine the optimal product mix by means of the application of linear programming techniques. (Hint: Start with your objective function and all necessary constraints.)In the Erlang loss model, system A has 5 servers and an implied utilization of 125 percent,while system B has 15 servers and an implied utilization of 125 percent. Which of thefollowing statements is true?a. System A has the higher utilization because it has fewer servers relative to the potentialdemand.b. The two systems have the same utilization because they have the same implied utilization.c. System B has a higher utilization because the fraction of lost demand is lower in that system.d. More information is needed to determine which system has the higher utilization.
- THE PINEAPPLE HARVESTING SEASON IN BACOLOD IS SHORT , AND MOST FARMERS DELIVER THEIR TRUCKLOADS OF PINEAPPLE TO A GIANT CENTRAL STORAGE BIN WITHIN A TWO - WEEK SPAN . BECAUSE OF THIS , PINEAPPLE - FILLED TRUCKS WAITING TO UNLOAD AND RETURN TO THE FIELDS HAVE BEEN KNOWN TO BACK UP FOR A BLOCK AT THE RECEIVING BIN . THE CENTRAL BINJ IS OWNED COOPERATIVELY, AND IT IS TO EVERY FARMER'S BENEFIT TO MAKE THE UNLOADING/STORAGE PROCESS AS EFFICIENT AS POSSIBLE. THE COST OF PINEAPPLE DETERIORATION CAUSED BY UNLOADING DSELAYS AND THE COST OF TRUCK RENTAL AND IDLE DRIVER TIME ARE SIGNIFICANT CONCERNS TO THE COOPERATIVE MEMBERS . ALTHOUGH FARMERS HAVE DIFFICULTY QUANTIFYING CROP DAMAGE, IT IS EASY TO ASSIGN A WAITING AND UNLOADING COST FOR TRUCK AND DRIVER OF P 18 PER HOUR . THE STORAGE BIN IS OPEN AND OPERATED 16 HOURS PER DAY AND 7 DAYS PER WEEK DURING THE HARVEST SEASON AND IS CAPABLE OF UNLOADING , 35 TRUCKS PER HOUR ACCORDING TO AN EXPONENTIAL DISTRIBUTION . FULL TRUCKS ARRIVE ALL…In 2015, the Phoenix/Zweig Advisors Zweig Total Return fund (ZTR) was expected to yield 5% and the Madison Asset Management Madison Strategic Sector Premium fund (MSP) was expected to yield 7%. You would like to invest a total of up to $60,000 and earn at least $3,500 in interest. Draw the feasible region that shows how much money you can invest in each fund (based on the given yields). Find the corner points of the region. Make sure you use a test point in your work. Shade the region(s) that is NOT the solution and label the region SOLUTION SET.3.3 4.manufactures 37-in. high def LCD tvs in 2 separate locations, Locations I and II. The output at Location I is at most 6000 televisions/month, whereas the output at Location II is at most 5000 televisions/month. TMA is the main supplier of tvs to the Pulsar Corporation, its holding company, which has priority in having all its requirements met. In a certain month, Pulsar placed orders for 3000 and 4000 televisions to be shipped to two of its factories located in City A and City B, respectively. The shipping costs (in dollars) per television from the 2 TMA plants to the 2 Pulsar factories are as follows. To Pulsar Factories From TMA City A City B Location I $7 $3 Location II $8 $9 TMA will ship x televisions from Location I to city A and y televisions from Location I to city B. Find a shipping schedule that meets the requirements of both companies while keeping costs to a minimum. (x,y)= What is the minimum cost? 6.Solve the linear programming problem by…
- Use the minimum-entry and u-v methods to solve the following minimum-cost transportationproblem. Assuming there is no cost associated with the artificial warehouse or market.Use Bland’s rule to choose entering and leaving variables where variables/cells are ordered from topto bottom and left to right.Emily Wye is currently working on the production schedules for next month. Her firm manufactures two types of ceramic grids: Type A £ Type B £ Selling price 60 70 Material X1 (at £2 per kg) 3 6 Material X2 (at £5 per kg) 10 10 Direct labour (grade 1) 12 9 Direct labour (grade 2) 10 15 Variable overhead 5 7 Notes: Labour rates and maximum labour hours available in the next month are: Grade Hourly rate Max. monthly hours…Suppose that in a certain year, the Phoenix/Zweig Advisors Zweig Total Return fund (ZTR) was expected to yield 4%, and the Madison Asset Management Madison Strategic Sector Premium fund (MSP) was expected to yield 9%. You would like to invest a total of up to $60,000 and earn at least $4500 in interest. Draw the feasible region that shows how much money you can invest in each fund (based on the given yields). (Place ZTR on the x-axis and MSP on the y-axis.). Find the corner points of the region. (Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.) (x, y)= ( ) (x, y)= ( ) (x, y)= ( )