Linear Programing Problem 12/3/2015

Binary Programing

Question 1 A professor has been contacted by four not-for-profit agencies that are willing to work with student consulting teams. The agencies need help with such things as budgeting, information systems, coordinating volunteers, and forecasting. Although each of the four student teams could work with any of the agencies, the professor feels that there is a difference in the amount of time it would take each group to solve each problem. The professor's estimate of the time, in days, is given in the table below Teams Budgeting Information Volunteers Forecasting A 32 35 15 27 B 38 40 18 C 41 42 25 D 45 30 1, Define the linear programing model with its decision variables and its constraints. 2 Use the computer solution generated by Excel (Solve) to see which team works with which project

Product Mix

Question 2 Chemco produces a chemical mixture for a specific customer in 1000 pound batches. The mixture contains three ingrediants zinc, mercury, and potassium. The mixture must conform to formula specifications that are supplied by the customer. The company wants to know the amount of each ingredient it needs to put in the mixture that will meet all the requirements of the mix and minimize total cost. The mixture must contain at least 200 pounds of mercury, 300 pounds of a zinc, 100 pounds of potassium, and the ratio of potassium to the other two ingredients cannot exceed 1 to 4. The cost per pound of mercury is 400; the cost per pound of zinc, 180, and the cost per pound of potassium, 90. Formulate a linear programming model and solve by using a computer.

selection

Question 3 M. Quinn is preparing for a 12 day dog sled race. He owns eight dogs, but the race will allow only five dogs – the four pack dogs and the lead dog. M. Quinn has developed a test to measure the endurance of each dog. The endurance score for each dog and the amount of ALPO each dog requires per day is listed in the table below. M. Quinn wants to select the five dogs that will give the team the maximum endurance score subject to the following constraints.   Only 62 ounces of ALPO will be available each day. At least two of the five dogs selected must have lead dog ability Ren and Snippy are very close. Thus if Ren is selected for the team, Snippy must also be selected for the team and vice versa. Snoopy and Snert hate each others guts. Therefore, either Snoopy can be on the team, Snert can be on the team, or neither of them can be on the team. However, both of them can not be on the team. Formulate the integer LP problem to determine which dogs should be selected in order to maximize endurance rating. Dog Endurance rating Ounces of Alpo/day Lead dog ability Bolivar 50 12 Yes Pluto 90 11 No Ren 65 10 No Lassie 95 15 Yes Odie 60 8 No Snippy 65 11 No Snoopy 90 15 Yes Snert 80 18 No Which dogs should not be included on the team? __________ What is the total maximum endurance for the team? ________ How many ounces of ALPO will actually be needed each day? _________

Vendor

Question 4 A store purchases two products (Product 1 and Product 2) that it stocks from three different vendors (Vendor A, Vendor B and Vendor C). The suppliers have limited capacity, and no one supplier can meet all of demand of Acme Mexico City. In addition, the vendors charge different prices for the products as shown in the table below: Vendor's Price Product A B C 1 $12 $13 $14 2 $10 $11 $10 Each vendor has a limited capacity in terms of the total number of products it can supply. However, as long the store provides sufficiently advanced orders, each supplier can devote its capacity to product 1, product 2, or any combination of the two products, if the total number of units ordered is within its capacity. Vendor capacities are as follows. Vendor A B C Capacity 600 1000 800 The demand at the store is 1000 units of product 1 and 800 units of product 2 . The purchasing manager wants to determine an optimal - ie, a lowest-cost - buying plan that would determine how many (>= 0) of each product should be bought from each vendor. To help the purchasing manager: 1) Develop an LP model for the above problem.