Question

For this​ problem, use the fact that the expected value of an event is a probability weighted​ average, the sum of each probable outcome multiplied by the probability of the event occurring.

You wish to hire Ron to manage the Dallas operations of your company. The profits from the operations depend partially on how hard Ron​ works, as follows.

	Probabilities
	Profit equals=​ $15,000	Profit equals= ​$55,000
Lazy	60​%	40​%
Hard worker	30​%	70​%

If Ron is​ lazy, he will surf the Internet all​ day, and he views this as a zero cost opportunity.​ However, Ron would view working hard as a​ "personal cost" valued at

​$1,500.

What fixed percentage of the profits should you offer​ Ron? Assume Ron only cares about his expected payment less any​ "personal cost."

You should offer Ron at least ______% of the profits. ​(Round your response to two decimal​ places.)

Answer 1

Expected value of profits,

if Ron is lazy = 15000 * 60% + 55,000 * 40%

= 9,000 + 22,000 = $31,000

if Ron is Hard-working = 15,000 * 30% + 55,000 * 70%

= 4,500 + 38,500 = 43,000

Difference in the above = 43,000 - 31,000 = 12,000

Now, personal cost as viewed by Ron = 1,500

So, you should offer Ron at least = 1,500 / 12,000 = 12.50% of profits so that Ron cares about his expected payment less any personal cost.

If there is any doubt please ask in comments

Thank you please rate