Let's solve the problem step by step. ### **Step 1: Write the constraints in standard form** We need to convert all inequalities to equalities by adding slack variables. #### **Given Linear Program:** Maximize: \[ 5A + 2B \] Subject to: 1. \( 1A - 2B \leq 400 \) 2. \( 2A + 3B \leq 610 \) 3. \( 6A - 1B \leq 125 \) 4. \( A, B \geq 0 \) #### **Add slack variables (\(S_1, S_2, S_3\))** 1. \( 1A - 2B + S_1 = 400 \) 2. \( 2A + 3B + S_2 = 610 \) 3. \( 6A - 1B + S_3 = 125 \) 4. \( A, B, S_1, S_2, S_3 \geq 0 \) ### **Step 2: Write the objective function in standard form** The slack variables do **not** appear in the original objective function, so their coefficients are 0. So, Maximize: \[ 5A + 2B + 0S_1 + 0S_2 + 0S_3 \] --- ### **Step 3: Fill in the blanks (as per your image)** #### **Objective function:** - \( \text{Max } 5A + 2B + (0)S_1 + (0)S_2 + (0)S_3 \) #### **Constraints:** - \( 1A - 2B + S_1 = 400 \) - \( 2A + 3B + S_2 = 610 \) - \( 6A - 1B + S_3 = 125 \) - \( A, B, S_1, S_2, S_3 \geq 0 \) --- ### **Final Answers for the Boxes:** - **Objective function:** \( 0 \) for \( S_1 \), \( S_2 \), \( S_3 \) - **First constraint:** \( S_1 \) - **Second constraint:** \( S_2 \) - **Third constraint:** \( S_3 \) --- ### **Summary Table:** | | Coefficient in Objective | Appears in Constraint | |-----------------|-------------------------|-------------------------| | \( S_1 \) | 0 | 1st | | \( S_2 \) | 0 | 2nd | | \( S_3 \) | 0 | 3rd | --- If you need to enter the values in the boxes as per the screenshot: - First row (Objective): **0**, **0**, **0** - First constraint: **S1** - Second constraint: **S2** - Third constraint: **S3** --- **If you need the standard form written out explicitly:** Maximize: \[ 5A + 2B + 0S_1 + 0S_2 + 0S_3 \] Subject to: \[ 1A - 2B + S_1 = 400 \\ 2A + 3B + S_2 = 610 \\ 6A - 1B + S_3 = 125 \\ A, B, S_1, S_2, S_3 \geq 0 \]