Let's break down the problem using linear programming.

Problem Analysis:

The candy company is producing two types of mixes:

• First Mix:

  • Contains: 1/2 nuts and 1/2 raisins.
  • Sells for: $7 per kg.

• Second Mix:

  • Contains: 3/4 nuts and 1/4 raisins.
  • Sells for: $9.50 per kg.

The company has 132 kg of nuts and 84 kg of raisins available. We need to figure out how many kilograms of each mix they should prepare for maximum revenue.

Let:

• $x_1$ = kilograms of the first mix (1/2 nuts, 1/2 raisins).
• $x_2$ = kilograms of the second mix (3/4 nuts, 1/4 raisins).

Constraints:

The total amount of nuts and raisins used must not exceed the available resources:

1. Nuts Constraint: The amount of nuts used in both mixes must be ≤ 132 kg. $\frac{1}{2}x_1 + \frac{3}{4}x_2 \leq 132$

2. Raisins Constraint: The amount of raisins used in both mixes must be ≤ 84 kg. $\frac{1}{2}x_1 + \frac{1}{4}x_2 \leq 84$

Objective Function:

The objective is to maximize revenue: $\text{Revenue} = 7x_1 + 9.5x_2$

This forms a linear programming model that we can solve for maximum revenue.

Would you like me to solve this step by step or use a more advanced method to get the answer?

Once I solve this, I can also tackle part (b) where the second mix price changes. Let me know!