To solve part (c), we need to determine the optimum solution using the Simplex method. Here’s the problem and step-by-step approach:

Problem Overview:

Reddy Mikks produces interior and exterior paints using two raw materials, $M_1$ and $M_2$. The table provides the resource constraints and the profit:

Resource Constraints:

• Maximum daily availability of raw material $M_1$ = 24 tons
• Maximum daily availability of raw material $M_2$ = 6 tons

Let:

• $x_1$ = tons of exterior paint produced per day
• $x_2$ = tons of interior paint produced per day

Objective Function:

The objective is to maximize the daily profit: $\text{Maximize } z = 5x_1 + 4x_2$

Constraints:

The production is subject to the availability of raw materials:

1. For $M_1$: $6x_1 + 4x_2 \leq 24$
2. For $M_2$: $1x_1 + 2x_2 \leq 6$
3. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

Simplex Method:

1. Formulation in Standard Form: To apply the Simplex method, we convert inequalities into equalities by adding slack variables: $6x_1 + 4x_2 + s_1 = 24$ $x_1 + 2x_2 + s_2 = 6$ where $s_1$ and $s_2$ are slack variables representing unused resources for $M_1$ and $M_2$, respectively. The objective function remains the same: $\text{Maximize } z = 5x_1 + 4x_2$

2. Initial Simplex Tableau: We can now set up the initial tableau for the Simplex method.