4. The Rossler Metal Machining Company produces widgets according to customer or

Question

4. The Rossler Metal Machining Company produces widgets according to customer order. The company has determined that widgets can be produced on three different machines: M1, M2, or M3. An analysis of widget production cost reveals the following data: Machine M1 M2 SCS Fixed Cost per Order Variable Cost per Unit S300 1,000 500 S9 a. Determine the breakeven point (in number of widgets produced) between Ml and M2. b. Determine the range of values (in number of widgets produced) that will lead to the preference of each machine based on minimizing total cost of an order. Hint: Sketch a plot. 1500 50 300 150

Explanation / Answer

Solution:

(a) The breakeven point (in number of widgets produced) between M1 and M2, is calculated as below:

Let the number of units at the break-even point = N

At the break-even point, the total costs of both the machines M1 and M2 will be equal, that is;

Total cost of machine M1 = Total cost of machine M2

$300 + ($9 x N) = $1000 + ($1 x N)

$300 + $9 N = $1000 + $ N

$8 N = $700

N = 87.5 or 88 units (rounding off to the next whole number)

Number of units at break-even point between M1 and M2 = 88 units

(b) The breakeven point (in number of widgets produced) between M2 and M3, is calculated as below:

At the break-even point, the total costs of both the machines M2 and M3 will be equal, that is;

$1000 + ($1 x N) = $500 + ($5 x N)

$1000 + N = $500 + 5N

4N = $500

N = 125

Number of units at break-even point between M2 and M3 = 125 units

The breakeven point (in number of widgets produced) between M1 and M3, is calculated as below:

At the break-even point, the total costs of both the machines M1 and M3 will be equal, that is;

$300 + ($9 x N) = $500 + ($5 x N)

$300 + 9N = $500 + 5N

4N = $200

N = 50

Number of units at break-even point between M1 and M3 = 50 units

Therefore, the range of values that will lead to the preference of each machine based on minimizing total cost of an order is given as;

M1 = 0 to 50 units

M2 = 125 units and above

M3 = 50 to 125 units

(c) For an order size of 75 units, M3 machine should be used to produce the order.

Total production cost using M3 machine for 75 units is calculated as;

Total production cost = $500 + ($5 x N)

Total production cost = $500 + ($5 x 75)

Total production cost = $500 + $375

Total production cost = $875

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