Beaver Creek Pottery

To make a model, we're going to make the decision variables, identify them first, then the objective, and then the constraints. The beaver creek pottery makes bowls and mugs. The two limited resources are clay and labor hours. The company wants to know how many bowls and mugs to make in order to maximize profit. There are 120 pounds of clay and 40 hours of labor. Okay, so they want to maximize profit. That's going to be our objective. How many bowls and mugs? That's going to be our decision variables. How many bowls for x1 and how many mugs for x2? The limited clay and limited labor will be our constraints. Okay, so here's a table that shows how much of each thing is made and needed. A bowl requires one hour per bowl, four pounds of clay per bowl, and each bowl makes $40. A mug requires two hours of labor, three pounds of clay, and a mug makes $50. Okay, so this is called a product mix. How many bowls and mugs should be made to maximize profit, given our constraints? Okay, so what resource do we have? 40 hours of labor per day, and we also have 120 pounds of clay. Let x1 be the n x2 is the n Okay, so we saw in our previous table that a bowl makes $40, a mug makes $50. So our objective is to maximize z equals $40 times each bowl, plus $50 times each mug, is how much profit will be. Okay, what about labor? Okay, let's go back to look at labor. Okay, how much labor is needed? One hour per bowl plus two hours per mug. So our labor constraint for labor is one times x1 plus two times x2, one hour per bowl plus two hours per mug, and we only have 40 hours, so it needs to be less than or equal to 40. Okay, our other constraint is limited clay. Let's go back and look at our table. Clay, we need four pounds per bowl and three pounds per mug for clay. So what is our clay constraint? Four times the non-negativity means x1 and x2 represent things, so those must be greater than or equal to zero. Okay, and this is just a s Maximize 40x1 plus 50x2 subject to those constraints. Okay, and x1 represents the n