Chapter 3.12, Problem 2P

Explanation of Solution

Formulation of Linear Programming (LP):

• Assume the following,
  • Let “${\text{JAN}}_1$”, “${\mathrm{FEB}}_1$”, “$MA{R}_1$”, “$AP{R}_1$”, “$MA{Y}_1$”, and “$JUN{E}_1$” be the number of computers that are rented for one month at the beginning of January, February, March, April, May, and June respectively.
  • Let “$JA{N}_2$”,“$FE{B}_2$”, “$MA{R}_2$”, “$AP{R}_2$”, “$MA{Y}_2$”, and “$JUN{E}_2$” be the number of computers that are rented for two month at the beginning of January, February, March, April, May, and June respectively.
  • Let “$JA{N}_3$”,“$FE{B}_3$”, “$MA{R}_3$”, “$AP{R}_3$”, “$MA{Y}_3$”, and “$JUN{E}_3$” be the number of computers that are rented for three months at the beginning of January, February, March, April, May, and June respectively.
  • Let “${\text{I}}_{\text{JAN}}$”, “${\text{I}}_{\text{FEB}}$”, “${\text{I}}_{\text{MAR}}$”, “${\text{I}}_{\text{APR}}$”, “${\text{I}}_{\text{MAY}}$”, and “${\text{I}}_{\text{JUNE}}$” be the number of computers that are available to achieve the demand on the month of January, February, March, April, May, and June respectively.
• The objective function to minimize the cost of renting the computers that are required is as follows,

$\begin{array}{c}{\text{Min z=200(JAN}}_1{\text{+FEB}}_1{\text{+MAR}}_1{\text{+APR}}_1{\text{+MAY}}_1{\text{+JUNE}}_1\text{)}\\ {\text{+350(JAN}}_2{\text{+FEB}}_2{\text{+MAR}}_2{\text{+APR}}_2{\text{+MAY}}_2{\text{+JUNE}}_2\text{)}\\ +450({\text{JAN}}_3{\text{+FEB}}_3{\text{+MAR}}_3{\text{+APR}}_3{\text{+MAY}}_3{\text{+JUNE}}_3\text{)}\\ -{\text{150MAY}}_3-300{\text{JUNE}}_3-175{\text{JUNE}}_2\end{array}$

• The above function subject to the following conditions,
  • “${\text{I}}_{\text{JAN}}={\text{JAN}}_1+{\text{JAN}}_2+{\text{JAN}}_3$” that represents the number of computers that are available to achieve January demand