Department of Management, UTSC MGTC74C Analysis for Decision Making – L30 Assignment #1 – Fall 2012 • Due Monday Oct. 1, 2012 in class. Late assignments will not be accepted. Please clearly put your section number on your assignment. Problem 1 The Whitt Window Company is a company with only 3 employees which makes 2 different kinds of hand-crafted windows: a wood-framed and an aluminum-framed window. They earn $60 profit for each wood-framed and $30 profit for each aluminum-framed window. Dough makes the wood frame and can make 6/day. Linda makes the aluminum frames, and can make 4/day.

Bob forms and cuts the glass, and can make 48 square feet of glass per day. Each wood-framed window uses 6 square feet of glass and each aluminum-framed window uses 8 square feet of glass. The company wishes to determine how many windows of each type to produce per day to maximize total profit. Formulate an LP model for this problem. Solve the problem using LINGO, Assume that solution does not have to be integers. Hand in your code and output. (5 + 3 = 8 marks) Problem 2 Max Z =8X1 + 5X2 s. t. X1 + X2 ? 6 9X1 + 5X2 ? 45 X1, X2 ? 0 (a) Solve the problem the graphical method presented in class.

Put x1 on X-axis. Clearly mark the feasible region and direction of increase/decrease of Z and state what the optimal solution is. Compute the Slack/Excess for each constraint. (7 + 1= 8 marks) (b) Determine range of objective function coefficient for X2 for which the current solution will remain optimal. (5 marks) (c) Determine range of objective function coefficient for X1 for which the point (5,0) will be optimal. (5 marks) (d) Determine the new optimal solution if 9×1 + 5×2 ( 45 became 9×1 +5 x2 ( 40? What is the dual price for this constraint? (5 + 2 = 7 marks)