Acme Manufacturing Inc. 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 expected production cost and the expected capacity for

producing these items.

Month

$1234$

Demand $($units$)420580310540$

Production cost per unit $($$$)49454647$

Production Capacity $($units$)500520450550$

Acme 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,

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. It also wants to maintain a safety stock

of at least $50$ units per month. Acme 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. Formulate the problem as an LP model. $($Do not solve it using excel solver$)$