You are an experienced machinist with a small tool shop. You have been asked to
ID: 352542 • Letter: Y
Question
You are an experienced machinist with a small tool shop. You have been asked to submit a bid to produce 15 special clamps for a new die that is under construction. You estimate that the material costs (metal & fasteners) for each clamp are $140. You also estimate that 10 labor hours are needed to produce the first clamp. The value of your labor is $50/hour. From similar orders in the past, you estimate that there is an 85% learning curve for this type of work.
a. What is the lowest total bid you should submit if you charge a 10% markup on material and you wish to recoup your labor costs?
b. Your potential customer is receptive to you bid from part a, but is hesitant to award you the order because the average cost per clamp that you bid 5% higher than his target. You respond to the customer that if they would increase their order from 15 clamps to x clamps, you could beat his target price. What is x?
Explanation / Answer
a)
with 85% learning rate, the time to make the clamp comes down by 15% per clamp made.
1st clamp = 10 hours
2nd clamp = 85%*10 = 8.5 hours
3rd clamp = 85%*8.5 = 7.23 hours
similarly we calculate the time taken for all as shown in table:
total time taken to make 15 clamps = 60.84 hours = 61 hours
material costs = 140*15 = 2100
10% markup = 10%*2100 + 2100 = 2310
labor costs = 61*50 = 3050
total price to be bid = 2310 + 3050 = 5360
b)
Here if we have x clamps
the xth clamp will take = 10*0.85(x-1) hours
total time taken to make x clamps = sum of all these terms 10*0.85(x-1) , x = 1,2,...x
this is a GP series = 10(1-0.85x)/(1-0.85) = 10*(1-0.85x)/(0.15)
current average cost = 5360/15 = 357.33
5% less = 357*95% = 339.5
total price for x clamps = 339.5*x
total material cost = 140*x*1.1 ...........(1.1 for 10% markup)
total labor cost = 50*10*(1-0.85x)/(0.15)
Now, 339.5x = 140*x*1.1 + 50*10*(1-0.85x)/(0.15)
339.5x - 154x = 500*(1-0.85x)/(0.15)
185.5x = 3333.33*(1-0.85x)
for x = 17 this is approximately solved
hence 17 clamps to ordered for discounted price
Clamp number time taken 1 10 2 8.50 3 7.23 4 6.14 5 5.22 6 4.44 7 3.77 8 3.21 9 2.72 10 2.32 11 1.97 12 1.67 13 1.42 14 1.21 15 1.03Related Questions
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