Question

In: Operations Management

Answer all three of the following Roman Numeral Questions (I, II, III). Equal credit. I. Suppose...

Answer all three of the following Roman Numeral Questions (I, II, III). Equal credit.

I. Suppose a company has a design maximum output of 200. Its actual output is 150 and its efficiency is 75%. Calculate its effective output and its capacity utilization.

II. Suppose a company has a fixed cost of $200,000 and a variable cost per unit of $14. It sells its product for $19.

a. Calculate its break-even level of output.

b. Calculate how much it must produce to make $100,000, assuming it can sell it all. Extra credit – 15 points. If it can outsource, and buy the product wholesale from a distributor at $16 each, over what level of output should it buy from the wholesaler, and over what level should it produce on its own?

III. If a company knows that its new employees have a seventy-five percent learning rate, and the first time they perform the task it takes 200 hours.

a. How long will it take to perform the eighth repetition?

b. How long will it take to perform the first eigth repetitions, cumulative?

Expert Solution

1. Design maximum output= 200

Actual Output=150

Efficiency=75%

Actual Output = Effective Output * Efficiency

Effective Output= Actual Output / Efficiency = 150/0.75 = 200

Capacity Utilization = (Actual Output/Potential Output)*100

= (150/200)*100=75%

2. Fixed cost = $200,000

Variable cost/ unit = $14 per unit

Sales price = $19 per unit

Contribution margin = Sales price – Variable cost = 19-14 = $5

Break even point = Fixed cost / Contribution margin

= 200000/5 = 40000 units

To make profit = $100,000, let the products sold be x

19x – (200,000 + 14x) = 100,000

5x -200,000= 100,000

5x = 300,000

x= 300,000/5 = 60,000 units

3. Learning rate = 75%

b= log learning rate / log 2 = log 0.75 / log 2 = -0.415

t₁= 200 hrs

a. t₈= t₁ * n^b = 200 * (8)^(-0.415) = 84.381 hrs

b.

Unit	Unit Time	Cumulative Time
t1	200	200
t2	150	350
t3	126.77	476.77
t4	112.5	589.27
t5	102.55	691.82
t6	95.08	786.9
t7	89.189	876.089
t8	84.38	960.469

Cumulative time for the first eight repetitions = 960.469 hours

keosha answered 1 year ago

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