Problem 7-8 Johnson Plastics makes and sells, among many other things, specialty
ID: 345619 • Letter: P
Question
Problem 7-8
Johnson Plastics makes and sells, among many other things, specialty plastic display cases for retail stores. Johnson’s expected annual demand for the display cases is 2,800 units, and average daily demand is 8 units. The production process is most efficient when 15 units per day are produced at a cost of $135 per unit. Setup cost is $11. Inventory carrying cost at Johnson is determined to be 10 percent annually.
a. What is the best production order quantity? (Round up your answer to the next whole number.)
Production order quantity _____ units
b. How many days is a required production run? (Round your answer to 3 decimal places.)
Number of days _______
Explanation / Answer
To be calculated:
(a) Best production order quantity
(b) Number of days in production run
Given values:
Annual demand, D = 2,800 units
Average daily demand, d = 8 units
Daily production, p = 15 units
Cost, C = $135 per unit
Setup cost, S = $11
Inventory carrying cost or Holding cost, H = 10% of 135 = $13.5
Solution:
(a) The production order quantity is calculated as;
Qp = (2*D*S) / H*(1 - d/p)
where, Qp = production order quantity
D = Annual demand
S = Setup cost
H = Holding cost
d = Daily demand
p = Daily production
Putting the given values in the above formula, we get;
Qp = (2*D*S) / H*(1 - d/p)
Qp = (2*2800*11) / 13.5*(1 - 8/15)
Qp = 61600 / 6.305
Qp = 9770.024 = 98.843
Production order quantity, Qp = 99 units
(b) Number of days in production run is calculated as;
Number of days = Production order quantity / Daily demand
Number of days = Qp / d
Number of days = 99 / 8
Number of days in production run is 12.375 days.