Question $1(25$ points$)$

The operations manager of an electronics firm wants to develop a production plan for the next six months. Projected orders for the company's products are listed below along with the direct cost of production in each month. The plan must specify the monthly amount $($in integers obviously$)$ to produce so that all demand is met. Shortages are not permitted. Any amount produced in excess of demand can be stored in inventory for later use at a cost of $$\frac{4}{?}$ unit$/$month$.$ Initial and final inventories are $0.$

$\backslash$table$[[$Month$,$Demand $($Units$),$Production cost $($$$/$unit$)],[1,1300,100],[2,1400,90],[3,1000,90],[4,800,120],[5,1700,105],[6,1900,90]]$

In addition to the direct costs of production and inventory, overhead costs must be charged for the maximum production level obtained and the maximum inventory level obtained during the $6-$month period. The following information should be used.

$($i$)$ Overhead cost for production $=$$$300($maximum production level$).$

$($ii$)$ Overhead cost for inventory $=$$$100($maximum level of inventory$).$

These costs are charged only once during the $6-$month period.

$($a$)(15$ points$)$ Set up an integer programming model that determines the minimum cost plan. Define your decision variables clearly.

$($b$)(10$ points$)$ Solve the model you developed in part $($a$)$ using OpenSolver and report the optimal solution. Upload the excel file as well when uploading your solutions. $($Hint: Optimal objective function value is $$1,304,220)$