JL.53 Bob's Bumpers has a repetitive manufacturing facility in Kentucky that makes automobile bumpers and other auto body parts. The facility operates 360 days per year and has annual demand of 77,000 bumpers. They can produce up to 350 bumpers each day. It costs $88 to set up the production line to produce bumpers. The cost of each bumper is $129 and annual holding costs are $39 per unit. Setup labor cost is $20 per hour.
(a) Based on the above information, what is the optimal size of the production run for bumpers? display answer to two decimal places
(b) Based on your answer to the previous question and assuming the manufacturer holds no safety stock, what would be the average inventory for these bumpers?
(c) Based on your answer two questions back, how many production runs would be required each year to satisfy demand?
(d) Suppose the customer (an auto manufacturer) wants to purchase these bumpers in lots of 500 and that bob's bumper is able to reduce setup cost to the poi t where 500 is now the optimal production run quantity. how much will they save in annual holding cost with this new lower production quantity?
(e) How much will they save in annual set up costs with this new lower production quantity?

The equilibrium production is the level in the production market where other things remain the same the level of production or output must vary with the change in single variables.

a) The optimal size of the production is 2,255.66

b) The average inventory will be 70.49

c) Number of production run are 33.25

d) Saving in annual holding cost will be 390.625

e) Saving in annual set up is 1,371.625

Computations:

a)

[tex]\begin{aligned}\text{Optimal size of the production run}&= \sqrt{\frac{(2\times\text{D}\times\text{S})}{\text{h}\times(1-(\frac{\text{d}}{\text{p}}))}}\\&=\sqrt{\frac{2\times75,000\times53}{25\times\left(1-\left(\frac{300}{320} \right ) \right )}}\\&= 2255.659549\;\text{or}\;255.66\end{aligned}[/tex]

were,

D is an annual demand

d is a daily demand

S is ordering cost

h is holding cost

p is a daily production rate

b)

[tex]\begin{aligned}\text{Average Inventory}&=\frac{\text{Maximum Inventory}}{2}\\&=\frac{\text{EPQ}\times\left(1-\left(\frac{\text{d}}{\text{p}} \right ) \right )}{2}\\&=\frac{2,255.66\times\left(1-\left(\frac{300}{320} \right ) \right )}{2}\\&=70.49\end{aligned}[/tex]

c)

[tex]\begin{aligned}\text{Number of production runs}&=\frac{\text{Annual Demand}}{\text{EPQ}}\\&=\frac{75,000}{2,255.66}\\&=33.25\end{aligned}[/tex]

d)

[tex]\begin{aligned}\text{Holding cost with EPQ} \left(2,255.66\right)&=\text{Average Inventory}\times\text{Holding Cost}\\&=70.49\times\$25\\&=\$1,762.25\end{aligned}[/tex]

[tex]\begin{aligned}\text{Holding Cost with EPQ}\left(500 \right )&=\frac{\text{EPQ}\times\left(1-\left(\frac{\text{d}}{\text{p}} \right ) \right )}{2}\times\text{Holding Cost}\\&=\frac{500\times\left(1-\left(\frac{300}{320} \right ) \right )}{2}\times\$25\\&=390.625\end{aligned}[/tex]

e)

[tex]\begin{aligned}\text{Savings}&=\text{Holding Cost with EPQ of 2,255.66}-\text{Holding Cost with EPQ of 500}\\&=\$1,762.25-\$390.625\\&=\$1,371.625\end{aligned}[/tex]

To know more about equilibrium production, refer to the link:

https://brainly.com/question/14449756