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Question 1137189: Eastern Cable and Com Switch are two companies specializing in digital switching systems. Eastern Cable is currently trading for $42 per share, and ComSwitch is currently trading for $27 per share. But in the near future the price of Eastern Cable will go up to $55 per share and Com Switch will go up to $43 per share. A client can invest a maximum of $50,000 in the two companies. The client wants to invest at least $15,000 in Eastern Cable and at least $10,000 in ComSwitch. Because of the higher risk associated with ComSwitch, the financial advisor has recommended that at most $25,000 should be invested in ComSwitch. Determine the number of shares of Eastern Cable and the number of shares of ComSwitch that will meet the investment constraints and maximize the total return for the investment.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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:
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.
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