Question 1 City Manufacturing has four machines for producing a particular computer chip. The production manager has to decide on the machine(s) to use for producing 1650 units of the chip. Machine 1s production capacity is between 300 and 1500 units. Machine 2 and/or Machine 3 can be used only if Machine 1s production is greater than or equal to 1000 units. Machine 4 can be used with no restrictions and can make any number of units. City Manufacturing has to pay a fixed cost if the machine is in operation. In addition, a variable cost per unit will be incurred. Machine Fixed cost ($) Variable cost per unit ($) Min. production Max. production 1 500 2.00 300 1500 2 800 0.50 500 1200 3 200 3.00 100 800 4 50 5.00 - - The objective of City Manufacturing is to minimize the total cost by meeting the production requirements. (a) Write down the integer linear program to determine the optimal production plan. [Hint: Use an additional binary variable to indicate when Machines 2 and 3 can be used.] (25 marks) (b) Develop an Excel spreadsheet model and use Solver to compute the optimal production plan and the minimum total cost. (Request Excel Keep Solver Solution, and generate Answer Report) (You have to submit the Excel file for grading. Screencap the Solver Parameter sub-window whenever appropriate.) (10 marks)

City Manufacturing has four machines for producing a particular computer chip. The production manager has to decide on the machine(s) to use for producing 1650 units of the chip. Machine 1's production capacity is between 300 and 1500 units. Machine 2 and/or Machine 3 can be used only if Machine 1's production is greater than or equal to 1000 units. Machine 4 can be used with no restrictions and can make any number of units. City Manufacturing has to pay a fixed cost if the machine is in operation. In addition, a variable cost per unit will be incurred. The objective of City Manufacturing is to minimize the total cost by meeting the production requirements. (a) Write down the integer linear program to determine the optimal production plan. [Hint: Use an additional binary variable to indicate when Machines 2 and 3 can be used.] (25 marks) (b) Develop an Excel spreadsheet model and use Solver to compute the optimal production plan and the minimum total cost. (Request Excel "Keep Solver Solution", and generate "Answer Report") (You have to submit the Excel file for grading. Screencap the "Solver Parameter" sub-window whenever appropriate.) (10 marks)