Assignment:
A small home-based company produces both hand-painted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week.
Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters.
Then graph the system of inequalities.
Provide complete and step by step solution for the question and show calculations and use formulas.