Question 1137189
x = number of shares of eastern cable.
y = number of shares of com switch.


constraint equations are:


42 * x + 27 * y <= 50,000 (total cost less than or equal to 50,000)
42 * x >= 15,000 (at least 15,000 in eastern cable)
27 * y >= 10,000 (at least 10,000 in com switch)
27 * y <= 25,000 (no more than 25,000 in com switch)


objective function:


maximize profit of 13 * x + 16 * y


using the desmos.com calculator, you will graph the opposite of the inequalities.


the region of feasibility will not be shaded.


the maximum profit function will be evaluated at the corner points of the feasible region to determine which corner point provides the maximum profit.


my graph looks like this:


<img src = "http://theo.x10hosting.com/2019/032241.jpg" alt="$$$" >



evaluating the profit function of 13 * x + 16 * y at each of the corner points, i get:


22552.91 at (595.238,925.926)
19457.675 at (357.143,925.926)
10568.779 at (357.143,370.37)
18306.873 at (952.381,370.37)


the maximum profit is 22,552.91 at the point (595.238,925.926).


that's 595.238 shares of eastern capital at a profit of 13 each and 925.0926 shares of com switch at a profit of 16 each.


the profit per share at eastern capital was calculated as 55 - 42 = 13.
the profit per share at com switch was calculated as 43 - 27 = 16.