Question

Please show your work so I can understand this portion, Thank you!

JL.51 Carl's Custom Cans produces small containers which are purchased by candy and snack food producers. The production facility operates 260 days per year and has annual demand of 13,800 units for one of its custom cans. They can produce up to 120 of these cans each day. It costs $43.31 to set up one of their production lines to run this can. (Carl pays $18 per hour for setup labor.) The cost of each can is $1.80 and annual holding costs are $2.30 per can. What is the optimal size of the production run for this can? (Display your answer to the nearest whole number). 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.) Number Suppose the customer for this custom can wants to purchase in quantities of 800 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.) Number 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.) Number

Answer 1

1st question

Economic production quantity(EPQ) = Sqrt(((2*D*Co)/Ch)*(p/(p-d)) where p = production rate = 120, d = daily demand = Annual demand/no of working days = 13800/260 = 53.07692308,D = annual demand = 13800

,Co = ordering cost = 43.31, Ch = holding cost = 2.3

Economic production quantity = Optimal production lot size = SQRT(((2*13800*43.31)/2.3)*(120/(120-53.07692308))) = 965.3557501 = 965 (Rounded to nearest whole number)

2nd question

Number of production runs = Annual demand/Optimal production lot size = 13800/965.3557501=14.29524815 = 15 (Rounded to next whole number)

3rd question

Total cost with EPQ =(1/2)(EPQ/p)(p-d)Ch+(D/EPQ)Co = (1/2)(965.3557501/120)*(120-53.07692308)*2.3+(13800/965.3557501)*43.31 = 1238.254395

To have order quantity 800 as optimal production quantity, total cost with quantity 800 needs to be 1238.254395

Let, reduced order cost with this = S

So, 2*(Annual demand/production quantity)*S = 1238.254395

or, 2*(13800/800)*s = 1238.254395

or, s = 1238.254395/34.5 = 35.89143174

Required set up cost = 35.89 (Rounded to 2 decimal places)

4th question

As Carl pays $18 per hour for setup labor, time it should take to set up this production line = (35.89/18) = 1.993888889 hour = 1.993888889*60 minutes = 119.6333333 minutes = 120 minutes (rounded to nearest whole number)