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Acme Manufacturing makes a variety of household appliances at a single manufacturing facility. The expected demand for one of these appliances during the next 4 months is shown in the following table along with the expected production costs and the expected capacity for producing these items.

Month

1

2

3

4

Demand

420

580

310

540

Production Cost

\$49.00

\$45.00

\$46.00

\$47.00

Production Capacity

500

520

450

550

Acme estimates it costs \$1.50 per month for each unit of this appliance carried in inventory at the end of each month. Currently, Acme 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. They also want to maintain safety stock of at least 50 units per month (minimum inventory at the end of the month). Acme wants to determine how many of each appliance to manufacture during each of the next 4 months to meet the expected demand at the lowest possible total cost.

Provide the complete linear programing formulation. Clearly specify decision variables, objective function and constraints.
Build a model in Excel and paste a screenshot here. Use “FORMULATEXT” in your model to show calculations.
According to Excel Solver, what is the optimal production plan for Acme Manufacturing? What is the minimum total cost?
Use SolverTable to investigate the effect on the total cost of changes in the initial inventory from 0 units to 120 units in increments of 20.

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