Question

. Example 13 Use the method of corners to solve the following linear programming problem. You want to invest up to $20,000 in two stocks: Coboll Inc. and EDGE. Each share of CoBoll Inc. stock costs $50, while cach share of EDGE stock costs $25. You must purchase at least twice as many shares of CoBoll Inc. stock as you do of EDGE stock, with a minimum of 100 shares of CoBoll Inc. According to a safety index.cach share of CoBoll Inc, has a safety number of 3 and each share of EDGE has a safety number of 2 How many shares of each stock should you purchase to minimize your investment's overall safely number? (Note: A lower safety number means less risk.) The set up below is similar to the set up we found in Section 3.1. What do our variables here represent? Objective: Minimize S = 3x + 2y What do each of our inequalities represent? Subject to: 50.x + 25y = 20000 Fo x -2y 20 => Saba -x+zy6o CPP |y20 Solution: Do you have any money leftover that was not invested, when you invest in a way to minimize your risk?

Answer 1

Answer.

X= quantity of shares of CoBoll Inc.

Y= quantity of share of EDGE.

S= investment's overall safety number.

Each of the inequality is the constraint that must be considered to minimise the risk.

First inequality represent that maximum amount available for the investment in two type of shares is 20,000 given the prices of each share.

Second, represents that shares purchased of CoBoll Inc . should be at least twice of EDGE shares.

Third, represents that the amount of CoBoll shares purchased should be atleast 100.

And last shows that amount of shares of EDGE purchased should be equal to or greater that 0.

For the last part, we will plot the constraints on the graph and find out optimal solution to minimize the risk.

In the graph below, when we plot the graph for all constraints, we get 4 feasible solutions.

Since, it can be seen that S is minimum at point (100,0).

So, a person will buy 100 shares of CoBoll Inc. in order to minimise his risk, and he will only spend the sum of $5000 given the price of share. He will be left with the sum of $15000.