Question

JL.51 Carl's Custom Cans produces small containers which are purchased by candy and snack food producers. The production facility operates 250 days per year and has annual demand of 12,000 units for one of its custom cans. They can produce up to 110 of these cans each day. It costs $58.51 to set up one of their production lines to run this can. (Carl pays $16 per hour for setup labor.) The cost of each can is $2.20 and annual holding costs are $2.70 per can.

What is the optimal size of the production run for this can? (Display your answer to the nearest whole number).
   

Given your answer to the previous question, how many production runs will be required each year in order to meet the annual demand? (Round your answer UP to the next whole number.)
   

Suppose the customer for this custom can wants to purchase in quantities of 600 units. What is the required setup cost to make this order quantity an optimal production run quantity for Carl's Custom Cans? (Display your answer to two decimal places.)
   

Based on your answer to the previous question (reduced setup cost), how long (in minutes) should it take to set up this production line? (Display your answer to the nearest whole number.)
  

Answer 1

What is the optimal size of the production run for this can?

Economic production quantity(EPQ) = Square root (((2*D*Cs)/Ch)*(p/(p-d)) where p = production rate = 110, d = daily demand = 12000/250 = 48
,D = annual demand = 12000
,Cs = setup cost = 58.51, Ch = holding cost = 2.7

Economic production quantity = Optimal production lot size = SQRT(((2*12000*58.51)/2.7)*(110/(110-48))) = 960.5927083 = 961 (Rounded to nearest whole number)

how many production runs will be required each year in order to meet the annual demand?

Number of production runs = Annual demand/Optimal production lot size = 12000/960.5927083 = 12.49228721 = 13 (Rounded to next whole number)

Suppose the customer for this custom can wants to purchase in quantities of 600 units. What is the required setup cost to make this order quantity an optimal production run quantity for Carl's Custom Cans? (Display your answer to two decimal places.)

Let, required ordering cost os S for which holding and setup cost will be same for optimal production size and 600 units in a lot.[As purchase cost will remain same irrespective of order size]

So, (1/2)*(960.5927083/110)*(110-48)*2.7+(12000/960.5927083)*58.51 = (1/2)*(600/110)*(110-48)*2.7+(12000/600)*S

or, 1461.847449 = 456.5454545 + 20S

or, S = (1461.847449-456.5454545)/20 =50.26509973 = 50.27 (Rounded to 2 decimal places)

Based on your answer to the previous question (reduced setup cost), how long (in minutes) should it take to set up this production line? (Display your answer to the nearest whole number.)

As Carl pays $16 per hour for setup labor, time it should take to set up this production line = (50.26509973/16) = 3.141568733 hour = 3.141568733*60 minutes = 188.494124 minutes = 188 minutes (rounded to nearest whole number)