Viking Manufacturing makes a variety of household appliances at a single manufacturing facility. The expected demand for one of these appliances during the next four months is shown in the following table along with the expected production costs and the expected capacity for producing these items.

Month

$1234$

Demand $420580310540$

Production Cost $$49\mathrm{.}00$ $$45\mathrm{.}00$ $$46\mathrm{.}00$ $$47\mathrm{.}00$

Production Capacity $500520450550$

Viking Manufacturing estimates it costs $$1\mathrm{.}50$ per month for each unit of this appliance carried in inventory $($estimated by averaging the beginning and ending inventory levels each month.$)$ Currently, Viking has $120$ units in inventory on hand for this product. To maintain a level workforce, the company wants to produce at least $400$ units per month. The company also wants to maintain a safety stock of at least $50$ units per month. Viking wants to determine how many of each appliance to manufacture during each of the next four months to meet the expected demand at the lowest possible total cost.

Create a spreadsheet model for this problem in excel and solve it using solver. The optimal solutions should only contain integer values since we are determining the number of inventories $($Make it an ILP problem$).$

The completed spreadsheet containing the optimal solution should be submitted as a $.$xlsx file.

Gradings will be based on the completeness of the excel formulas, and the specification for the solver.