Acme estimates that it costs $1.50 per month for each unit of this appliance car

Question

Acme estimates that it costs $1.50 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, Acme 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
know how many appliances to manufacture during each of the next 4 months to meet
expected demand at the lowest cost.

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

a. Formulate the problem as a linear program .
b. Create a spreadsheet model for this problem and solve it with Solver.
c. What is the optimal solution?

Explanation / Answer

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 I understand everything except the first sentence. Can someone please explain the meaning of the first sentence. total cost (each month) = production cost + inventory cost first sentence refers to inventory cost calculation build total cost equation month by month then add all months: month #1: production cost1 = P1*(49.00) inventory cost1 = (1/2)*(120 + (120 + P1 - D1))*(1.50) ...since currently have 120 in stock etc determine constraints based on capacity limits, minimum production goals, and safety stock requirement Doesn't the inventory level depend of whether delivery happens continuously or at the end of the month ? Or is this assumed by convention to be one or the other of the two ? Originally Posted by geosonel total cost (each month) = production cost + inventory cost first sentence refers to inventory cost calculation build total cost equation month by month then add all months: month #1: production cost1 = P1*(49.00) inventory cost1 = (1/2)*(120 + (120 + P1 - D1))*(1.50) ...since currently have 120 in stock etc

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