Formulation of a Linear Programming (LP) to maximize total profit earned from Erica’s investment:

Let “x₁” be the number of dollars invested in stocks.

The “x₂” be the number of dollars invested in loans.

As every dollar invested in stocks gives 10 cents profits, so the total profit on stocks would be $0.1x₁. Likewise, the total profit on loan would be $0.15x₂.

Since the objective is to maximize total profit earned from Erica’s investment, the objective function is defined as follows:

$Max Z=0.10x1+0.15x2$

Constraint 1:

At least, 30% of total invested money must be invested in stocks. The “x₁+ x₂” is the total money invested in the investment. Since the number of dollars invested in stocks must be at least 30% of the total investment, the constraint is defined as follows:

$x1≥0.3(x1+x2)0.7x1−0.3x2≥0$

Constraint 2:

At least, $400 of all money must be invested in loans, so the constraint is defined as:

$x2≥400$

Constraint 3:

At most, $1000 is invested in stocks and loans, so the constraint is defined as:

$x1+x2≤1000$

Therefore, the formulation to the given linear program is:

$Max Z=0$

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Solution Summary: The author explains the objective function of a linear program to maximize total profit earned from Erica’s investment.

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