$\"\"$

\

Let $\"\"$ be the units of the Gourmet Dog food.

\

Let $\"\"$ be the units of the Chow Hound food.

\

Cost of each can of Gourmet Dog is $\"\"$ cents with $\"\"$ units of vitamins and $\"\"$ calories.

\

Cost of each can of Chow Hound is $\"\"$ cents with $\"\"$ units of vitamins and $\"\"$ calories.

\

Total cost of sixty cans is $\"\"$ .

\

Hence the constraint is $\"\"$ and $\"\"$ .

\

Kevin $\"\"$ s dog has at least $\"\"$ units of vitamins.

\

Hence the constraint is $\"\"$ .

\

Kevin $\"\"$ s dog has at least $\"\"$ units of calories.

\

Hence the constraint is $\"\"$ .

\

$\"\"$

\

The objective function is $\"\"$ .

\

The constraints are

\

$\"\"$

\

Graph :

\

Graph the inequalities and shade the required region.

\

$\"\"$

\

Note : The shaded region is the set of solution points for the objective function.

\

Observe the graph:

\

Tabulate the solutions of each of two system of inequalities and obtain the intersection points.

\ \

\ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\

System of boundary

\

equations

\

\

$\"\"$

\

$\"\"$

\

\

$\"\"$

\

$\"\"$

\

\

$\"\"$

\

$\"\"$

\

\

$\"\"$

\

$\"\"$

\

Solution (vertex points)

\"\"

\"\"

\"\"

\

$\"\"$

\

\

$\"\"$

\

Find the value of objective function at the solution points.

\

At point $\"\"$ , $\"\"$ .

\

At point $\"\"$ , $\"\"$ .

\

At point $\"\"$ , $\"\"$ .

\

At point $\"\"$ , $\"\"$ .

\

Observe the values of $\"\"$ :

\

The minimum value of $\"\"$ is $\"\"$ at $\"\"$ .

\

Therefore, Kevin should take $\"\"$ cans of Gourmet Dog and $\"\"$ cans of Chow Hound for total cost of $\"\"$ .

\

$\"\"$

\

Kevin should take $\"\"$ cans of Gourmet Dog and $\"\"$ cans of Chow Hound for total cost of $\"\"$ .