PLEASE USE LINGO SOLVER FOR THE SOLUTION

1. (15 marks) Nancy is planning a birthday party for two friends born on the same month and day. There will be just one cake, with blue candles for Stephanie and red candles for William, one for each year. Stephanie will be 50, and William will be 52. Nancy goes to the store and finds that Type A boxes of candles sell for $7, and contain 20 blue candles and 15 red ones, while Type B boxes of candles sell for $5, and contain 6 blue candles and 11 red ones. She doesn't want to carry more than five boxes home. If you wish, print this page to use the graphpaper below. 4 X2 3 2 1 1 1 1 0 0 1 2 3 4 5 6 X (a) Defining variables X1 and X2, formulate this integer model. 2 (b) On a 6 by 4 graph, plot the constraints, show the feasible region for the con- straints, show all the feasible dots for integer solutions, and the trial and optimal isovalue lines. By inspection, state the optimal values for X1, X2, and compute the OFV. 2. (20 marks) A firm wishes to produce a single product at one or more locations so that the total monthly cost is minimized subject to demand being satisfied. At each location there is a fixed charge to be paid if any are produced (but is nil otherwise), and a variable cost which depends on whether the units are produced on regular time or on overtime. Each location has capacity restrictions on regular and overtime production. The relevant data are: Plant Location 1 2 3 4 5 6 Fixed Cost 2100 1900 2300 1700 2700 2000 Regular Time Overtime Unit Cost Capacity Unit Cost Capacity 3.80 1200 4.60 500 2.90 1500 4.10 600 4.20 1800 5.60 800 3.40 2000 4.20 550 3.60 2900 5.10 650 3.10 3000 4.90 900 Demand is for 8000 units per month. (a) Write the algebraic model for this problem. You are not required to submit this part, except that the list of variables must be submitted in Word or pdf, or these must appear at the top of the file in part (b). (b) Solve the model using LINGO or the Excel Solver. (c) State the solution in words