Ph.D. Preliminary Examination – June 2013 (11:00 am to 4:00 pm) Candidate Name: ________________________ Answer ALL Questions Sensitivity Analysis (20 points) The Whitt Window Company is a company with only three employees which makes two different kinds of hand-crafted windows: a wood-framed and an window. They earn $60 profit for each wood-framed window and $30 profit for each aluminum-framed window. Doug makes wood frames and can make 6 per day. Linda makes the aluminum frames and can make 4 per 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 of glass and each aluminum-framed window uses 8 square feet of glass. (2 points) Formulate a linear programming model for this problem. (2 points) Use the graphical method to solve the problem. (3 points) Find the range for the profit from aluminum-framed window for which the current solution will remain optimal. (3 points) Bob may reduce his working hours or stay for overtime to decrease/increase the available glass per day. Find the range for available glass (in square feet) that will keep the same optimal solution mix. (2 points) Bob is willing to stay for overtime. What is the maximum amount that you would be willing to pay for an hour given that Bob can make 6 square feet in one hour during the overtime? (1 points) Bob is staying for an extra hour at a rate of $20 and makes additional 6 square feet of glass. What is the net change in profit? (2 points) Write the dual problem. (3 points) Solve the dual graphically and state the optimal objective value. (Hint: You may eliminate one variable (or two variables) using the information from the primal solution.) (2 points) Using Part (g), state the change in profit if Doug can produce 7 wood frames in one day.
Ph.D. Preliminary Examination – June 2013 (11:00 am to 4:00 pm) Candidate Name: ________________________ Answer ALL Questions Sensitivity Analysis (20 points) The Whitt Window Company is a company with only three employees which makes two different kinds of hand-crafted windows: a wood-framed and an window. They earn $60 profit for each wood-framed window and $30 profit for each aluminum-framed window. Doug makes wood frames and can make 6 per day. Linda makes the aluminum frames and can make 4 per 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 of glass and each aluminum-framed window uses 8 square feet of glass. (2 points) Formulate a linear programming model for this problem. (2 points) Use the graphical method to solve the problem. (3 points) Find the range for the profit from aluminum-framed window for which the current solution will remain optimal. (3 points) Bob may reduce his working hours or stay for overtime to decrease/increase the available glass per day. Find the range for available glass (in square feet) that will keep the same optimal solution mix. (2 points) Bob is willing to stay for overtime. What is the maximum amount that you would be willing to pay for an hour given that Bob can make 6 square feet in one hour during the overtime? (1 points) Bob is staying for an extra hour at a rate of $20 and makes additional 6 square feet of glass. What is the net change in profit? (2 points) Write the dual problem. (3 points) Solve the dual graphically and state the optimal objective value. (Hint: You may eliminate one variable (or two variables) using the information from the primal solution.) (2 points) Using Part (g), state the change in profit if Doug can produce 7 wood frames in one day.
prelim-or-2013.docx