1. An initial solution to a transportation problem is given below. a. Use Northwest, MCM and VAM to determine the initial solution b. Use the stepping stone method to detemine if the solution is optimal in VAM. c. Generate the optimal solution based on (b) в с Supply A B 50 l00 /00 1 110 200 300 200 160 10 |200 300 150 3 Demand 140 200 80 420 2)
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operations resereach1 - linear programming - transportation
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- What is the requirement of initial basic feasible solution in transportationProblem.1. Graph an isoprofit line (label as Line AA) that touches the feasible corner point that does not lie on either x-axis or y-axis. Secondly, graph the isoprofit line (label as Line ZZ) that touches the corner point where the optimal solution lies. 2. Provide the x-intercept and y-intercept of the isoprofit line AA.An advertising firm desires to reach two types of audiences-customers with annual income of more than K40,000 (target audience A) and customers with annual income of less than K40,000 (target audience B). The total advertising budget is K200, 000 . One programme of TV advertising costs K50, 000 while one programme of radio advertising cost K20, 000. Contract conditions ordinarily require that there should be at least 3 programmes on TV and not more than 5 on radio. Survey indicates that one TV programme reaches 750,000 customers in target audience A and 150,000 in target audience B. One radio programme reaches 400,000 customers in target audience A and 260,000 in target audience B. Formulate a linear programming model for this problem Use the simplex method to determine the media mix to maximize the number of customers reached.
- The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 760 homeless patients and no more than 800 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 2,100 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $9,800 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $7,800 per month. How many of each type of patient should it house in order to maximize profit? (If an answer does not exist, enter DNE.) high-income patients homeless patients profitThe Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 700 homeless patients and no more than 620 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $13,000 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $9,000 per month. How many of each type of patient should it house in order to maximize profit? Group of answer choices A)700 homeless patients and 1,100 high-income patients B)1,200 homeless patients and 600 high-income patientsC)700 homeless patients…The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 700 homeless patients and no more than 620 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $13,000 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $9,000 per month. How many of each type of patient should it house in order to maximize profit?
- The Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 750 homeless patients and no more than 900 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $9,500 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $8,000 per month. How many of each type of patient should it house in order to maximize profit? HINT [See Example 3.] (If an answer does not exist, enter DNE.) high-income patients: homeless: profit:Are you able to use complementary slackness and your answer to part (a) to find solution(s) to the primal LPP? Why or why not?answer to part (a): attached here No, it does not have an optimal solution.The Green Company manufactures an electric motorcycle, which it sells through two of its company-owned retail stores. Store A has put in a request for between 40 and 50 of the motorcycles, inclusive, and Store B needs between 30 and 40 units, inclusive. On the basis of previous sales, the management of Green Company has decided that the number of motorcycles shipped to Store B should equal or exceed 40% of the number shipped to Store A by 20 units. The shipping costs from the manufacturer to Store A and Store B are $80 and $40 per motorcycle, respectively. How many motorcycles should the Green Company ship to each store in order to minimize its shipping costs? Store A motorcycles __________ Store B motorcycles __________ What is the minimum cost? $_____________
- 1) How many corner points are there in this LP problem?2) Which of the following points is a corner point in the feasible region which provides the optimal solution for this LP problem?3) Which of the following is the optimal value of the objective function for the LP model in this problem?4) Which of the following is the correct illustration of the feasible region for the given LP model below?Solve the following LP problems using graphical method. Clearly draw the feasible region, corresponding isoprofit (isocost) lines and find the optimal solution(s). Make the necessary conclusions about your result (e.g. unique optimal solution, multiple optimal solutions, etc.)Use the least optimal initial basic feasible solution from (a) as your starting point to find the optimal solution.