Chapter 4.16, Problem 3P

Explanation of Solution

Formulating preemptive goal programming:

Let,

$x_1$= Number of color TV.

$x_2$= Number of color VCR

${\text{S}}_{\text{i}}{}^{\text{-}}$= Amount by which are under the ${\text{i}}^{\text{th}}$ goal.

${\text{S}}_{\text{i}}{}^{+}$= Amount by which exceeds the ${\text{i}}^{\text{th}}$ goal.

$\text{z}$= penalty associated with meeting the chip requirements.

Consider the cost to purchase a color TV is 300 dollars and cost to purchase a voucher is 200 dollars. The maximum of amount that can be spend for purchasing is 20000dollrs. So, the constraint can be written as given below,

${\text{300x}}_{\text{1}}{\text{+200x}}_{\text{2}}{\text{+S}}_{\text{1}}{}^{\text{-}}{\text{-S}}_{\text{1}}{}^{\text{+}}\text{=20000}$

The sale of color TV earns a profit of 150dollars and the sale of VCR earns a profit of 100dollor and at least 11000dollors should be earned in profit from the sale. So, the constraints can be written as given below,

${\text{150x}}_1{\text{+100x}}_{\text{2}}{\text{+S}}_2{}^{\text{-}}{\text{-S}}_2{}^{\text{+}}\text{=11000}$

A color TV requires 3 square yard of storage space and VCR requires 1 square yard of storage space and no more than 200 square yard of storage space is required