Questions: Solve the following problem with Excel Solver: (Leave no cells blank - answers to 2 decimal places.) Minimize Z = 4A + 7B 3A + 12B ≥ 90 2A + 16B ≥ 64 1B ≥ 10

Transcript text: Solve the following problem with Excel Solver: (Leave no cells blank - answers to 2 decimal places.) \[ \begin{aligned} \text { Minimize } Z & =4 A+7 B \\ 3 A+12 B & \geq 90 \\ 2 A+16 B & \geq 64 \\ 1 B & \geq 10 \end{aligned} \]

Solution

Solution Steps

To solve this linear programming problem, we need to minimize the objective function \( Z = 4A + 7B \) subject to the given constraints. The constraints are linear inequalities that define the feasible region. We can use Python's optimization libraries to find the values of \( A \) and \( B \) that minimize \( Z \) while satisfying all constraints.

Step 1: Define the Objective Function

We want to minimize the cost function given by: \[ Z = 4A + 7B \]

Step 2: Identify the Constraints

The problem is subject to the following constraints: \[ \begin{aligned} 3A + 12B & \geq 90 \quad (1) \\ 2A + 16B & \geq 64 \quad (2) \\ B & \geq 10 \quad (3) \end{aligned} \]

Step 3: Solve the Linear Programming Problem

After solving the linear programming problem, we find the optimal values for \( A \) and \( B \): \[ A = 0.00, \quad B = 10.00 \]

Step 4: Calculate the Total Cost

Substituting the values of \( A \) and \( B \) into the objective function: \[ Z = 4(0) + 7(10) = 70.00 \]