A restaurant has decided to close the kitchen for an annual deep clean. It will take 24 hours to complete the deep clean. As the restaurant doesn't want to close for the time they decide to operate one oven and put on three special menus. The cost of the ingredients is $3 for menu 1, $15 for menu 2 and $2 for menu 3. The menu is priced at $9 for menu 1, $17 for menu 2 and $10 for menu 3. As there is only one oven available all meals must be cooked separately. It takes 4 hours for menu 1, one for the menu 2 and 3 for menu 3. The total time available in the oven is 24 hours. The chefs have 30 hours to prepare the food and it takes 2 hours to prepare menu 1, 6 for menu 2 and 3 for menu 3.
Formulate and solve, by hand, using the Simplex method the above as a Linear Programming problem in order to maximise profit for the restaurant.
From your final table identify:
(i) Optimum solution in full
(ii) Ranges for the Objective Co-efficients
(iii) Shadow Prices for all constraints
(iv) Right Hand Side Ranges for all constraints
Confirm your results by solving using a computer package of your choice.