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. (a) Defining variables X1 and X2, formulate this integer model. (b) On a 6 by 4 graph below, plot the constraints, show the feasible region for the constraints, 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. X2 4 3 2 1 1 T 2 3 4 5 6 X