12. In the electricity pricing model in Example 7.4, the demand functions have positive and negative coefficients of prices. The negative coefficients indicate that as the price of a product increases, demand for that product decreases. The positive coefficients indicate that as the price of a product increases, demand for the other product increases.
a. Increase the magnitudes of the negative coefficients from —0.013 and —0.015 to —0.017 and —0.020, and then rerun Solver. Do the changes in the optimal solution go in the direction you would expect? Explain.
b. Increase the magnitudes of the positive coefficients from 0.005 and 0.003 to 0.007 and 0.005, and then rerun Solver. Do the changes in the optimal solution go in the direction you would expect? Explain. c. Make the changes in parts a and b simultaneously, and then rerun Solver. What happens now?
6. In the truck-loading problem in Example 8.3, we assumed that any product could be loaded into any compartment. Suppose the following are not allowed: product 1 in compartment 2, product 2 in compartment 1, and product 3 in compartment 4. Modify the model appropriately, and then use Evolutionary Solver to find the new optimal solution. (Hint: Add a penalty to the objective for violating these new constraints.)