This may be more of a business question but given that it has integration this seemed to be the best place to post it. My problem is with part C. I believe parts 1 and 2 are correct but i am having trouble solving c.
A small hospital must order blood at $10/pint for a certain surgical procedure before the surgery begins. If the amount needed is less than what is ordered then the unused blood can be returned for $5/pint. On the other hand, if more blood is needed than what is ordered, a special emergency order must be placed with the local blood bank, which charges $25/pint plus a fixed charge of $40. The amount of blood needed is unknown and thus considered a random variable. Let y = amount ordered (pints), x = amount needed (pints). Assume that the patient’s treatment is independent of y, so that it is suitable to minimize the expected cost of supplying blood.
Let C(x,y) be the cost to the hospital when y is ordered and the amount x is needed. Write the mathematical expression for C(x,y).
My Answer: C(x,y)=C(y|x)=10*y+5(y-x) for y>x
C(x,y)=C(y|x)=10*y+25*(x-y)+40 for y<x
Write an expression for the expected cost if y is ordered,
.
My Answer:
=∫C(y|x)*fx(x) dx
If [FONT="][/FONT]
show that
My Answer: This is where i am stuck, however i try to solve it i am not getting the above equations. Any help is appreciated
A small hospital must order blood at $10/pint for a certain surgical procedure before the surgery begins. If the amount needed is less than what is ordered then the unused blood can be returned for $5/pint. On the other hand, if more blood is needed than what is ordered, a special emergency order must be placed with the local blood bank, which charges $25/pint plus a fixed charge of $40. The amount of blood needed is unknown and thus considered a random variable. Let y = amount ordered (pints), x = amount needed (pints). Assume that the patient’s treatment is independent of y, so that it is suitable to minimize the expected cost of supplying blood.
Let C(x,y) be the cost to the hospital when y is ordered and the amount x is needed. Write the mathematical expression for C(x,y).
My Answer: C(x,y)=C(y|x)=10*y+5(y-x) for y>x
C(x,y)=C(y|x)=10*y+25*(x-y)+40 for y<x
Write an expression for the expected cost if y is ordered,
My Answer:
If [FONT="][/FONT]
My Answer: This is where i am stuck, however i try to solve it i am not getting the above equations. Any help is appreciated