This problem is an example of a linear programming problem, where we aim to maximize the profit under certain constraints.

Let:

• $x_1$ be the number of units of solution A to produce daily.
• $x_2$ be the number of units of solution B to produce daily.

Objective function:

We want to maximize the total profit, which is given by: $\text{Maximize } Z = 8x_1 + 10x_2$ where $8x_1$ represents the profit from solution A and $10x_2$ represents the profit from solution B.

Constraints:

1. Availability of raw material /: The total amount of raw material / used by both solutions A and B must not exceed 150 units. The amount used by solution A is $0.5x_1$, and the amount used by solution B is $0.5x_2$. Therefore, the first constraint is: $0.5x_1 + 0.5x_2 \leq 150$ Simplifying: $x_1 + x_2 \leq 300$

2. Availability of raw material //: The total amount of raw material // used by both solutions A and B must not exceed 145 units. The amount used by solution A is $0.6x_1$, and the amount used by solution B is $0.4x_2$. Therefore, the second constraint is: $0.6x_1 + 0.4x_2 \leq 145$

3. Demand constraints:

   • The demand for solution A is between 30 and 150 units, so: $30 \leq x_1 \leq 150$
   • The demand for solution B is between 40 and 200 units, so: $40 \leq x_2 \leq 200$

Summary of the linear programming model:

• Objective: Maximize $Z = 8x_1 + 10x_2$
• Constraints: x_1 + x_2 &\leq 300 \\ 0.6x_1 + 0.4x_2 &\leq 145 \\ 30 \leq x_1 &\leq 150 \\ 40 \leq x_2 &\leq 200 \end{aligned}$$
• Non-negativity: $x_1 \geq 0, x_2 \geq 0$

This problem can now be solved using methods like the graphical method (if visualizing) or more commonly with Simplex method or using software like Excel's Solver or Python's libraries (like SciPy or PuLP).

Would you like me to solve it using one of these methods or assist further?