The RMC Corporation blends three raw materials to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of \(\frac{2}{5}\) ton of material 1 and \(\frac{3}{5}\) ton of material 3. A ton of solvent base is a mixture of \(\frac{1}{2}\) ton of material 1, \(\frac{1}{5}\) ton of material 2, and \(\frac{3}{10}\) ton of material 3.

RMC’s production is constrained by the limited availability of the three raw materials. For the current production period, RMC has the following quantities of each raw material:
- Material 1: 20 tons
- Material 2: 5 tons
- Material 3: 21 tons

Management wants to achieve the following P1 priority level goals:
- **Goal 1:** Produce at least 30 tons of fuel additive.
- **Goal 2:** Produce at least 15 tons of solvent base.

Assume there are no other goals. Is it possible for management to achieve both P1 level goals given the constraints on the amounts of each material available?

**Goal Programming Model:**

Let:
- \(x_1\) = the number of tons of fuel additive produced
- \(x_2\) = the number of tons of solvent base produced
- \(d_1^+\) = the amount by which the number of tons of fuel additive produced exceeds the target value of 30 tons
- \(d_1^-\) = the amount by which the number of tons of fuel additive produced is less than the target of 30 tons
- \(d_2^+\) = the amount by which the number of tons of solvent base produced exceeds the target value of 15 tons
- \(d_2^-\) = the amount by which the number of tons of solvent base is less than the target value of 15 tons

**Constraints:**
1. Material 1: \(\frac{2}{5}x_1 + \frac{1}{2}x_2 \leq 20\)
2. Material 2: \(\frac{1}{5}x_2 \leq 5\)
3. Material 3: \(\frac{3}{5}x_1 + \frac{3}{10}x_2 \leq 21\)
4. Fuel Additive Goal: \(x_1 + d_1^- - d_1^+ = 30\)
5. Solvent Base Goal: \(x_2 + d_2^- - d_2^+ = 15\)

Determine the optimal product mix while achieving both P1 priority level goals, considering that both goals are equally important to management.