Linear Algebraic Expression for Constraint

How to write a linear algebraic expression for the constraint related to the amount of fruit juice used in production?

Group of answer choices

1. (0.03* NO) + (0.02* NB)
2. (0.03* NO) + (0.02* NB) > 15
3. (0.03* NO) + (0.02* NB) ≤ 15
4. (0.03* NO) + (0.02* NB)< 15

Answer:

The correct linear algebraic expression for the given constraint "The amount of fruit juice used in production during the coming week cannot exceed 15 gallons" is (0.03 * NO) + (0.02 * NB) ≤ 15.

Explanation:

In the expression, NO represents the decision variable for one type of fruit juice used in production, while NB represents the decision variable for another type of fruit juice used in production. The coefficients 0.03 and 0.02 indicate the respective amounts of juice used per unit of NO and NB.

The inequality symbol "≤" signifies that the total of (0.03 * NO) and (0.02 * NB) should not exceed 15 gallons. This constraint ensures that the total amount of fruit juice used in production does not surpass the specified limit of 15 gallons.

The expression is a linear combination of the decision variables, where the coefficients and variables are multiplied and summed to form the constraint equation.