A company manufactures two sizes of paper cups, large and small, and uses a linear programming model to optimize the mix of sizes produced to maximize total operating profit. Each case of large cups sold generates an operating profit of $60, and each small cup generates an operating profit of $40. Producing a case of large cups requires 2.5 labor hours and $75 of material. Producing a case of small cups requires 1.5 labor hours and $50 of material. The plant has allocated a maximum of 1,000 labor hours and $40,000 of material to cup production. Sales contracts require that the company must produce at least 200 large cups and at least 100 small cups. Formulate the optimization problem to be solved by specifying the decision variables, the result variable, the objective, and the constraints.