An American automotive and energy company is currently one of the top five manufacturers of lithium ion batteries in the world. Lithium-ion batteries are commonly used for portable electronics and electric vehicles and are growing in popularity for military and aerospace applications. They have a high energy density, no memory effect, low self-discharge, and a significantly longer lifespan compared to conventional alkaline batteries. As with most manufacturing operations, each battery is tested as it comes off the production line. If a battery tests positive for defects, a series of more complex tests are administered to determine the nature of the defect and, hopefully, repair the battery. Therefore, some batteries that test positive can be repaired and eventually sold, while others must be scrapped completely. The Chief Operations Officer (COO) has asked the Director of Enterprise Analytics (DEA) to analyze current profit associated with defect-free batteries and the loss associated with defective batteries produced by the company. The DEA and her team found:

1) Defect-free batteries that initially test positive for defects eventually produce $1,780 in profit and occur 4.88% of the time, 2) Defect-free batteries that test negative for defects produce $2,230 in profit and occur 92.77% of the time, 3) Defective batteries that test positive for defects cost the company $3,410 and occur 1.59% of the time, 4) Defective batteries that test negative for defects eventually cost the company $9,790 and occur 0.76% of the time.

(a) What is the expected profit per battery from true negatives in the long run? (Round your answer to the nearest cent)

(b) What is the expected loss per battery from false negatives in the long run? (HINT: When we ask for the loss value, we are expecting a positive number. Enter a positive number here. This may change in your subsequent calculations.) (Round your answer to the nearest cent)

(c) What is the expected loss per battery from true positives in the long run? (HINT: When we ask for the loss value, we are expecting a positive number. Enter a positive number here. This may change in your subsequent calculations.) (Round your answer to the nearest cent)

(d) What is the expected profit per battery from false positives in the long run? (Round your answer to the nearest cent)

e) What is the expected profit per battery for all batteries (regardless of false positive, true positive, etc.) in the long run? (Keep in mind loss is negative profit)(Round your answer to the nearest cent)

Interpret the value you calculated above in part e by mentally inserting it into the blanks below (Select all that apply.).

This manufacturing process is expected to yield a gain of $_______ per battery on average in the long-run.This manufacturing process is expected to yield a loss of $_______ per battery on average in the short term.The expected profit is $_______.The expected loss is $_______.