As per the solution of exercise 14, we have

Maximize \[Z\text{ }=\text{ }200x\text{ }+\text{ }120y\]subject to constrains

\[3x\text{ }+\text{ }y\le 600\]…. (i)

\[x\text{ }+\text{ }y\le 300\]…. (ii)

\[x\text{ }\text{ }y\le -100\]…. (iii)

\[x\ge 0,\text{ }y\ge 0\]’Now, let’s construct a constrain table for the above

Next, solving equation (i) and (iii) we get

\[x\text{ }=\text{ }100\text{ }and\text{ }y\text{ }=\text{ }200\]

On solving equation (i) and (ii), we get

\[x\text{ }=\text{ }150\text{ }and\text{ }y\text{ }=\text{ }150\]

It’s seen that the shaded region is the feasible region whose corner points are \[O\left( 0,\text{ }0 \right),\text{ }A\left( 200,\text{ }0 \right),\text{ }B\left( 150,\text{ }150 \right),\text{ }D\left( 0,\text{ }100 \right)\].

Evaluating the value of Z, we have

From the above table it’s seen that the maximum value is \[48000\].

Therefore, the maximum value of Z is \[48000\] at \[(150,150)\] which means \[150\] sweaters of each type.