Minimum Premium Cases for Profit Target

A company produces two types of phone cases: standard cases and premium cases. The profit from each standard case is $3, and the profit from each premium case is $5. The company has a goal to achieve at least $600 in profit.

Let s represent the number of standard cases produced and p represent the number of premium cases produced. The company can produce a maximum of 200 cases of both types combined. This scenario can be represented by the following system of inequalities:

$$3s + 5p \geq 600$$

$$s + p \leq 200$$

$$s \geq 0, \ p \geq 0$$

Determine the minimum number of premium cases p that must be produced in order to meet the profit goal, considering the constraints provided. Report your answer as a number (either decimal or fraction).