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 $1\text{'}$s production capacity is between $300$ and $1500$ units. Machine $2$ and$/$or Machine $3$

can be used only if Machine $1\text{'}$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$)$