We're now going to set up the Product Mix problem in Excel. Let's take a look at a convenient way to do it. The table over here, shows the different products A, B, C, D, D2, E, and E2 and the machines M1, M2, and M3 in order to compute the profit contribution margins. Here are the values that we have from the table for A, the profit contribution margin is three dollar, for B it's three dollars, C its three dollar, for product D there are two variables, D standing for the production level up to 20 units. That's going to be three dollars if it's below 20 units, and then for any production above 20 units, which is captured by D2 it's contribution level is two dollars. Similarly for a product E, we have these two variables that have contribution margins of three dollar and two dollar to capture the nonlinear profit margins. Then the cost of running machine 1,2, and 3, that is a labor costs that's minus four dollar, minus four dollar, and minus three dollar for machine 3. These are highlighted in red because these are negative numbers. Here basically, these are minus 4, minus 4 and minus 3. These are our decision variables in, for these many decision variables that we have defined. When we are running the solver, we'll specify these cells as the ones containing the value of the decision variables should be stored. Then the profit is computed by looking at the objective function value Z, which is the product of the decision variable values times the contribution margin for each of them. That's going to be the sum product of these two rows and that's going to be stored over here, which is the objective function value. Now in terms of the constraint, we have some constraint of the values of D, E, and the number of hours that the machine is going to run. Here we have 20, which will be the upper bound for whatever value is stored in this cell. Similarly, here it's 20 the value that is going to be stored in the cell corresponding to the value of the decision variable E because it can go only up to 20 at most. These are going to be used for the constraints that D and E are less than equal 20 units, and then these cells have the value for the upper bound on the right-hand side of the number of hours that this machines can be run, which is 128. We will be using these cells and these values to specify those constraints. Next, we have the number of minutes that each product requires on the different machine. Product A requires 12 minutes on machine 1, eight minutes on machine 2 and five minutes on machine 3 and so on. We have those values from the big table that we had, and we're also going to use these values to define the three constraints that we got in the formulation. The sum product of these values in row 8, these values over here with the value of the decision variables, will be giving us the left-hand side of those constraint and the right-hand side value is equal to 0. If you recall the way the constraints were defined, we had them as equality, some expression equal to 0. We are going to be using the right-hand side to be equal to 0, and the left-hand side is the value of that expression. This is what the expression was 12A plus 7D plus 8C plus 10D plus 10D_2 plus 7E plus 7E_2 minus 60M_1 is equal to 0. In order to get this left-hand side of the expression, we would need to multiply the values over here with the corresponding values of the decision variables and add them up to get this left-hand side of the expression. It will be 12 times whatever is the value of A, plus 7 times whatever is the value of B and so on, minus 60 times M_1. Then since these coefficients we have put them at zero, these values don't matter for this left-hand side. The total sum product that we find by multiplying the individual elements with the corresponding element value in the cell of the decision variable and then taking the sum of these individual products, is going to be stored over here in cell L8. That created the left-hand side of the first constraint and that needs to be set to equal to 0 for the right hand side in the solver. Similarly for machine 2, we have this constraint, 8A plus 9B plus 4C plus 11E plus 11E_2 to minus 60M_2 equal to 0. We have these values over here. As you can see, this is 8 times A plus 9 times B plus 4 times C. Then these coefficients zero, so D doesn't appear, D_2 doesn't appear and then plus 11 times E, plus 11 times E_2, and then minus 60M_2, and that value is going to be stored here when we do the sum product. That has to be set equal to the right-hand side value, which is 0, and similarly for the third constraint. This is how we can set up the problem and now we can solve it using the solver tool in Excel.