Subjects optimization

Fungsi Tujuan Ae2Ad5

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1. The problem asks: How do you find the Fungsi Tujuan (Objective Function) in optimization problems? 2. The Fungsi Tujuan is a mathematical expression that represents the goal of the problem, usually to maximize or minimize some quantity. 3. To find the Fungsi Tujuan, identify what quantity you want to optimize. For example, in a business problem, it might be profit, cost, or revenue. 4. Express this quantity as a function of the decision variables. For example, if $x$ and $y$ are variables, the Fungsi Tujuan might be $Z = ax + by$ where $a$ and $b$ are coefficients representing contribution per unit. 5. The general form is: $$ \text{Fungsi Tujuan: } Z = c_1 x_1 + c_2 x_2 + \cdots + c_n x_n $$ where $c_i$ are constants and $x_i$ are variables. 6. Important rules: - Clearly define variables. - Understand what you want to optimize. - Write the function in terms of these variables. 7. Example: If you want to maximize profit from selling products A and B, and profit per unit is 5 and 3 respectively, then: $$ Z = 5x + 3y $$ where $x$ and $y$ are quantities of products A and B. 8. This function $Z$ is your Fungsi Tujuan. 9. In summary, find the quantity to optimize, define variables, and write the function expressing that quantity in terms of variables.