Step-by-step explanation:
To develop an aggregate plan, we need to consider the forecasted demand and available capacity while minimizing costs. Let's analyze the two scenarios:
a. Chase Plan:
In a chase plan, the production is adjusted to match the forecasted demand. This means that each month's production will be equal to the demand for that month. However, the regular output can be less than regular capacity.
Using the given regular output capacity of 130 engines per month, we can match the demand as follows:
Month | Forecasted Demand | Production (Chase Plan)
-----------------------------------------
Jan | 150 | 150
Feb | 110 | 110
Mar | 120 | 120
Apr | 140 | 140
May | 160 | 160
Jun | 180 | 180
Total cost for the chase plan:
= (Regular Production Cost + Overtime Production Cost)
= (150 * $60 + 0 * $90) + (110 * $60 + 0 * $90) + (120 * $60 + 0 * $90) + (140 * $60 + 0 * $90) + (160 * $60 + 0 * $90) + (180 * $60 + 0 * $90)
= $9,000 + $6,600 + $7,200 + $8,400 + $9,600 + $10,800
= $51,600
b. Level Plan:
In a level plan, we aim to maintain a constant production rate throughout the planning horizon, using inventory to absorb fluctuations in demand. Backlog should not exist in the last month.
To calculate the optimal production rate, we need to consider the carrying cost and backlog cost. Let's calculate the production rate based on these costs:
Carrying cost = $2 per engine per month
Backlog cost = $90 per engine per month
Total cost for the level plan:
= (Carrying Cost + Backlog Cost)
= (0 * $2 + 40 * $90) + (40 * $2 + 0 * $90) + (10 * $2 + 20 * $90) + (30 * $2 + 0 * $90) + (50 * $2 + 0 * $90) + (70 * $2 + 0 * $90)
= $3,600 + $800 + $2,200 + $60 + $100 + $140
= $6,900
Therefore, the total cost for the chase plan is $51,600, and the total cost for the level plan is $6,900.