A family-run business produces hand-crafted bowls and mugs from clay for sale at an artisans market. 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 week. Each bowl requires 600 grams of clay and 1.2 hours of labor, and yields a profit of $10. Each mug requires 400 grams of clay and 1.6 hours of labor, and yields a profit of $8. There are 36 labor hours and 12 kilograms of clay available each week for production. Formulate the linear programming model to determine the product mix that will maximize the business's weekly profit. Make sure to define the decision variables, the objective function, and all necessary constraints. Provide all constraints in standard form. You do not need to solve the LP