following Destination Supply Source 2 3 4 2 3 10 15 21 4 3 Demand 11 17 12 a) Formulate this problem as a linear program b) Find the initial basic feasible solution for the above transportation table. Obtain an optimal solution and compare the resulting number for the transportation model of each of the following methods and state which one will give you the most minimum results 1. Northwest corner rule. -23
Q: 1. Obtain the initial basic feasible solution to the following transportation problem using north…
A: We have the initial table as, We have Total supply = 14 + 16 + 5 = 35 and Total demand = 6 + 10 +…
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- Use the least optimal initial basic feasible solution from (a) as your starting point to find the optimal solution.In order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protein. But the rabbits should be fed no more than five ounces of food a day.Rather than order rabbit food that is custom-blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce. What is the optimal blend?In order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protein. But the rabbits should be fed no more than five ounces of food a day.Rather than order rabbit food that is custom‐blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce. What is the optimal blend? a. Choose the unknowns, i.e. variables. Statewhat they are so you know exactly whatyou are looking for.b. Write your OPTIMIZATION EQUATION. c. Write the constraints as a system ofinequalities, usually there are several.d. Graph the system and identify thefeasibility region. e. Identify the corners of the feasibilityregion, which will be…
- 1. Draw the feasible region of the LP. Label the constraints and corner points in your graph. 2. Is (5,5) a feasible region? How do you say so? 3. Enumerate all the feasible corner points of this LP. 4. What is the optimal solution? Provide x1,x2, and z value.A finished product weighs exactly 150grams. The two raw materials used in manufacturing theproduct are A, with cost of birr 2 per unit and B with a cost of birr 8 per unit. At least 14 units ofB and not more than 20 units of A must be used. Each units of A and B weighs 5 and 10 gramsrespectively.A. Formulate the above problem as a linear programing modelB. Obtain optimal solution to the problem by using the simplex method, how much ofeach type of row material should be used for each unit of the final product in orderto minimize the cost?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.
- The Metropolitan Bus Company (MBC) purchases diesel fuel from American Petroleum Supply. In addition to the fuel cost, American Petroleum Supply charges MBC $300 per order to cover the expenses of delivering and transferring the fuel to MBC’s storage tanks. The lead time for a new shipment from American Petroleum is 7 days; the cost of holding a gallon of fuel in the storage tanks is $0.04 per month or $0.48 per year. The annual fuel usage is 250,000 gallons. MBC buses operate 300 days a year.What is the optimal order quantity for MBC?(Is it 12,500 gallons?)How frequently should MBC place an order to replenish the gasoline supply?(Is it 25 days?)What is the reorder point? (5,000 gallons?)During each 6-hour period of the day, the Bloomington Police Department needs at least the number of policemen shown in the following table. Policemen can be hired to work either 12 consecutive hours or 18 consecutive hours. Policemen are paid $15 per hour for each of the first 12 hours a day they work and are paid $22.5 per hour for each of the next 6 hours they work in a day. Formulate an LP that can be used to minimize the cost of meeting Bloomington’s daily police requirements and solve it via Excel. Time Period Number of required policemen 12:00AM----6:00AM 12 6:00AM----12:00PM 8 12:00PM----6:00PM 6 6:00PM----12:00AM 15Find the feasible solution of the given problem using two methods: Least Cost Method Vogiel's Method/Penalty Method
- A company produces 2 (two) different grades of gasoline – regular and premium from 3(three)components (1,2,3). The company wants to determine the optimal mix of the three componentsin each grade of the gasoline that will maximize profit. The maximum quantities available for eachcomponent and their cost per gallon are as follows: Component Cost per gallon maximum gallons available per day1 2.50 5,0002 2.60 10,0003 2.84 10,000In order to ensure the appropriate blend, each grade has certain specifications as follows: Grade Component Specs Selling Price per gallon Regular At most 30% component 1…7. Use Lagrange multipliers to give an alternate solution. Find two positive numbers whose product is 100 and whose sum is a minimum.A marketing research group conducting a telephone survey must contact at least 150 wives and 120 husbands. It costs P100 to make a daytime call and (because of higher labor costs) P150 to make an evening call. On average, daytime calls reach wives 30% of the time, husbands 10% of the time, and neither of these 60% of the time, whereas evening calls reach wives 30% of the time, husbands 30% of the time, and neither of these 40% of the time. Staffing considerations mean that daytime calls must be less than or equal to half of the total calls made. How many should be interviewed at each period to minimize the cost of completing the survey? fomulate the LP Model; identify the decision variables used in the model; and determine the optimal solution using graphical method.