Answer
(a)
Provided that, a manufacturer manufactures x number of LCD televisions and y number of plasma televisions in a month and earned profit of \$125 per LCD television and \$200 per plasma television.
So, the objective function that describes his total monthly profit is:
\[z=125x+200y\]
(b)
Provided constraints are:
Factory equipment cannot make more than 450 LCD televisions in a month.
Factory equipment cannot make more than 200 plasma televisions in a month.
Manufacturing cost in unit is \$600 for per LCD televisions and \$900 for per plasma televisions and total manufacturing cost cannot exceed $360,000.
These constraints can be described as system of inequalities as follows:
\[\left\{ \begin{align}
& x\le 450 \\
& y\le 200 \\
& 600x+900y\le 360000 \\
\end{align} \right.\Rightarrow \left\{ \begin{align}
& x\le 450 \\
& y\le 200 \\
& 2x+3y\le 1200 \\
\end{align} \right.\]
Hence, the system of constraints is\[\left\{ \begin{align}
& x\le 450 \\
& y\le 200 \\
& 2x+3y\le 1200 \\
\end{align} \right.\].
Work Step by Step
Since,
from part (d), the maximum value of objective function is 77500 at \[\left( 300,200 \right)\].
So, refer part (d) to get the relevant values to fill in the blanks of the provided statement.
“The television manufacturer will make the greatest profit by manufacturing 300 LCD televisions each month and 200 plasma televisions each month. The maximum monthly profit is $77500.”
