Chapter 7, Problem 15PS

To determine

To sketch: a graph of inequalities that describes the amounts $t$and $a$of terrestrial and aquatic vegetation, respectively.

Explanation of Solution

Given information:

Each day, an average adult moose cab process about 32 kilograms of terrestrial vegetation and aquatic vegetation. From this food, it needs to obtain about 1.9 grams of sodium and 11000 calories of energy. Aquatic vegetation has about 0.15 gram of sodium per kilogram and about 193 calories of energy per kilogram, where as terrestrial vegetation energy has minimum sodium about four times as much energy as aquatic vegetation.

Calculation:

Given that moose can process 32kg of aquatic and terrestrial vegetation.

If $t$is the amount of terrestrial vegetation and $a$is the amount of aquatic vegetation intake then we can write,

  $a+t\le 32$

Also it needs 1.9 grasp of sodium which it should get only from aquatic vegetation, which contains 0.15gram per kilogram.

  $0.15a\ge 1.9$

Again it needs 11000 calories. Aquatic food gives 193 calories and terrestrial food gives 772 per kilogram.

  $193a+772t\ge 11000$ .

Since moose cannot consume negative quantity of food two additional constraints can also be added:

  $\begin{array}{l}a\ge 0\\ t\ge 0\end{array}$

The system of inequalities formed are:

  $\begin{array}{l}a\ge 0\\ t\ge 0\end{array}$

  $\begin{array}{c}a+t\le 32\\ 0.15a\ge 1.9\\ 193a+772t\ge 11000\end{array}$

The graph drawn is as shown below: