Q1. - Algebra 2

Question

1: Find the maximum and minimum value of a linear function subject to constraints is called (linear, polygonal) programming.

Step-by-Step Solution

Answer

Finding the maximum and minimum value of a linear function subject to constraints is called linear programming.

Step-1 –Taking an example to justify the statement

A sporting goods manufacturer makes a $\$5$profit on soccer balls and a $\$4$ profit on volleyballs. What is the function for the maximum and minimum value of profit.

Assumption profit on $1$soccer ball $=\$4.$

Step-2 –Assumption of variables

Let $x$and $y$be the number of soccer balls and volleyballs are produced.

Step-3 –Drafting the condition for maximum and minimum value of profit

Profit on $1$soccer ball $=\$5$

Profit on $x$ soccer ball $=\$5x$

Profit on $1$ volleyball $=\$4$

Profit on $y$volleyball $=\$4y$

So, the function of profit $=5x+4y.$