A family-run business produces bowls and mugs made from clay. The two resources needed to produce these goods are pottery clay and skilled labor. Given these limited resources, the business wishes to know how many bowls and mugs to produce each day. Each bowl requires 400 grams of clay and 1 hour of labor, and yields a profit of $8. Each mug requires 300 grams of clay and 2 hours of labor, and yields a profit of $10. There are 40 labor hours and 12 kilograms of clay available each day for production. Formulate the linear programming model to determine the product mix that will maximize the daily profit. Make sure to define the decision variables, the objective function, and all necessary constraints. You do not need to solve the LP.
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