Costal Cup Company wants to determine how many cases of large and small cups should be produced per day in order to maximize profit given the labor and material constraints.

- The unit profit value for large cups is $35 per case.
- The unit profit value for small cups is $30 per case.

Constraints:
- There are 120 hours of labor available per day.
- There are 2000 units of resin material available per day.
- There are 325 units of packaging material available per day.

Each case of large cups requires:
- 0.75 hours of labor
- 16 units of resin material
- 2.5 units of packaging material

Each case of small cups requires:
- 1 hour of labor
- 11 units of resin material
- 2 units of packaging material

Formulate a linear programming model for this problem to determine how many cases of large and small cups should be produced in order to maximize the total profit.

Solve this problem by using the graphing method OR by using Excel Solver.

What is the optimal solution?

The linear programming model aims to determine the optimal number of cases of large and small cups to be produced per day in order to maximize total profit for Costal Cup Company.

To solve the problem, a linear programming model is formulated. The decision variables are L and S, representing the number of cases of large and small cups to be produced, respectively. The objective function Z is defined as the total profit, given by the equation Z = 35L + 30S. The goal is to maximize this objective function.

The model is subject to constraints that ensure the utilization of available resources. The labor constraint states that 0.75L + S should be less than or equal to 120, representing the available labor hours per day. The resin material constraint states that 16L + 11S should be less than or equal to 2000, indicating the available resin material units. The packaging material constraint states that 2.5L + 2S should be less than or equal to 325, representing the available packaging material units.

Additionally, non-negativity constraints are included, stating that L and S should be greater than or equal to zero, as negative quantities are not feasible.

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