QUESTION FOUR

$($a$)$ Use the big $-M$ simplex method to

Minimize $Z=4x_1+x_2$

Subject $to3x_1+x_2=3$

$,4x_1+3x_{2}6$

$,x_1+2x_{2}3$

$,x_1,x_{2}0$

$($b$)$ The research department of Kwasa Kwasa Ltd has recommended to the marketing

department to launch a shampoo of three different types. The marketing manager has to

decide one of the types of shampoo to be launched under the following estimated pay offs

for various levels of sales:

What will be the marketing manager's decision if

i$.$ Maximin criterion is applied?

ii$.$ Minimax criterion is applied?

iii. Maximax criterion is applied?

iv$.$ Laplace criterion is used?

v$.$ Regret criterion is used?