Question

Need help within 30 minutes please!

JL.52 A producer of industrial climate control modules has recently changed to cellular manufacturing. The production facility operates 250 days per year and has annual demand of 6,500 units They can produce up to 80 modules each day. It costs $18.50 to set up a work cell to produce this module. The cost of each module is $32 and annual holding costs are $4 per unit. Setup labor cost is $14 per hour.

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

How much time (in minutes) does it take to set up a work cell? (Display your answer to two decimal places.)

Suppose the main customer for this module wants to purchase in quantities of 200 units. What is the required setup time (in minutes) to make this order quantity an optimal production run quantity? (Display your answer to two decimal places.)

Answer 1

Annual demand, D = 6500 units

Demand rate, d = 6500/250 = 26 units/day

Production rate, p = 80 units/day

Setup cost, S = $ 18.5

Annual holding cost, H = $ 4

1) Optimal size of the production run = sqrt(2DS/H/(1-d/p))

= sqrt(2*6500*18.5/4/(1-26/80))

= 298 units

2) Number of production runs per year = D/Q

= 6500/298

= 22 production runs

3) Time to setup a work cell = Setup cost / Setup labor cost

= 18.5/14

= 1.32 hours

= 79.29 minutes

4)

Required Setup cost, S = Q²*H*(1-d/p)/2D

= 200²*4*(1-26/80)/(2*6500)

= $ 8.31

Required setup time = 8.31/14

= 0.5934 hour

= 35.60 minutes