Chapter 6.12, Problem 7P

a.

Explanation of Solution

• When pricing out “${\text{w}}_{\text{j}}$” for “j=1,2”, the user can get the following,

$\begin{array}{l}\text{(Input}\text{j}\text{utilized}\text{by}\text{hospital}\text{1)}\left(\text{Hospital 1's dual price}\right)\text{+}\\ \left(\text{Input j utilized}\text{by hospital 3}\right)\text{(Hospital 3's dual price)+}\\ \left(\text{Dual price}{\text{of constraint 8w}}_{\text{1}}{\text{+ 15w}}_{\text{2}}\text{= 1}\right)\left(\text{Input j utilized by hospital 2}\right)\text{+}\\ {\text{(Dual price of w}}_{\text{j}}\ge \text{0}\text{.0001 constraint) =0}\end{array}$

• The input “j” utilized by composite hospital can be produced by rearranging this equality by transferring first two terms to the right hand side of the equality as follows,

$\begin{array}{c}{\text{Input j utilized by composite hospital=(Dual price of constraint (8w}}_{\text{1}}{\text{+ 15w}}_{\text{2}}\text{= 1})\end{array}$

b.

Explanation of Solution

Reasons:

• From the problem “5” in chapter 6.12 of the text book, the user can get the input “j” used by composite hospital as follows,

$\begin{array}{c}\text{Input j utilized by composite hospital=}\left(\text{Dual price of}{\text{constraint 8w}}_{\text{1}}{\text{+ 15w}}_{\text{2}}\text{= 1}\right)\left(\text{Input j utilized by hospital 2}\right)\\ \text{+ (Dual price of constraint}{\text{w}}_{\text{j}}\ge \text{0}\end{array}$