IMC, Inc. needs to schedule production of a certain item for the next four months. The unit cost is estimated to be $12 for the first two months and $14 for the last two months. From the company’s forecasting models, monthly demands are estimated to be 400, 750, 950, and 900 units, respectively. IMC can produce a maximum of 850 units each month on regular time. Overtime can be scheduled during the second and third months, which increases monthly capacity by 200 units. However, units produced on overtime cost $4 more to produce. Excess production can be stored at a cost of $3 per unit per month, but a maximum of 50 units can be stored during any month. Assuming that beginning and ending inventory levels are zero, how should the production be scheduled so as to minimize total costs?

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Answer:

The correct answer will be "$40,450".

Explanation:

According to the estimation given in the scenario,

The monthly demands are:

  • 400 units
  • 750 units
  • 950 units
  • 900 units

So, the total cost will be:

⇒ [tex](400\times 12) + (750\times 12) + (850\times 14) + (150\times 18) + (50\times 3) + (850\times 14)[/tex]

⇒  [tex]4800 + 9000 + 11900 + 2700 + 150 + 11900[/tex]

⇒  [tex]40,450[/tex] ($)