A street vendor in Nairobi City sells hot dogs and hamburgers. A hot dog gives a profit of Sh.0.60 and a hamburger gives a profit of Sh.0.50. Each hot dog uses Sh.1.20 worth of materials and each hamburger uses Sh.1.60 worth. There is only Sh.48 worth of materials currently on hand to make hot dogs and hamburgers. From previous experience the vendor knows that he should make at least 8 hamburgers and no more than 20 hot dogs. He also believes that he should make at most twice as many hot dogs as hamburgers. a. Solve the problem graphically, stating optimal values of the decision variables. What is the maximum profit? [15 Marks] b. How low would the profit for hot dogs have to drop before the vendor would stop making them? [2 Marks] c. The vendor remembers that he omitted the constraint that no more than 12 hamburgers should be produced, all other constraints remaining the same. With this new constraint in the model, what would the optimal solution be? What profit would the vendor make now? [ 3 Marks]