Objective Function: C = 6x – 4y

The objective function given is C = 6x - 4y.

An objective function represents the value that needs to be maximized or minimized in a mathematical model. In this case, "C" represents the value to be optimized, and it is a function of two variables, x and y.

The objective is to find the values of x and y that maximize or minimize the objective function C. To do this, you can use various optimization techniques such as linear programming, calculus, or graphical methods. The specific technique to be used depends on the context or problem at hand.

The objective function in this case is represented by the equation C = 6x - 4y, where C is the value of the objective function and x and y are the variables.

To understand the objective function, it's important to know that it is commonly used in optimization problems. In such problems, we aim to find the values of variables that maximize or minimize the objective function. In this case, we are trying to maximize or minimize the value of C.

The coefficients of the variables, 6 and -4, represent the weights given to each variable. A positive coefficient (such as 6 in this case) signifies that increasing the value of the variable will lead to an increase in the objective function. Conversely, a negative coefficient (like -4) indicates that increasing the variable will result in a decrease in the objective function.

For example, if we consider x as the number of units produced and y as the number of units sold, the coefficient 6 suggests that for every unit produced, the objective function will increase by 6 units. On the other hand, the coefficient -4 implies that for every unit sold, the objective function will decrease by 4 units.

To evaluate the objective function, substitute specific values for x and y into the equation. This will give you the corresponding value of C. The goal is to find the values of x and y that optimize the objective function and yield the largest or smallest value for C, depending on the context of the problem.

X >= 0

Y >= 0

Y <= 1/3X + 3

5 >= y + X