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MAT 540 Case Assignment #3 Julia’s Food Booth A. Formulate and solve a linear programming model for Julia that will help you advice her if she should lease the booth. JULIA’S PRODUCTSTORAGE VARIABLESCOST SELLING PRICE NEEDED PizzaX1$1. 33$1. 5014 inches Hot DogsX2$0. 45$1. 5016 square inches BarbecueX3$0. 90$2. 2525 square inches Maximize Z= $0. 75×1, 1. 05×2, 1. 35×3 $0. 75×1 + . 0. 45×2 + 0. 90×3 = 1,500 24×1 + 16×2 + 25×3 < 55,296 in2 of oven space. 1 > x2 + x3 >2. 0 x1, x2, x3 > 0 (A) Solution: x1 = 1,250 pizza slices x2= 1,250 hot dogs x3= 0 barbecue sandwiches Z= $2,250 B. If Julia were to borrow some more money from a friend before the first game to purchase more ingredients, could she increase her profit? If so, how much should she borrow and how much additional profit would she make? What factor constrains her from borrowing even more money than this amount (indicated in your answer to the previous question? | |Final |Reduced |Objective |Allowable |Allowable | |Name |Value |Cost |Coefficient |Increase |Decrease | |X1 |1250. 00 |0. 00 |0. 75 |1 |1. 00000001 | |X2 |1250. 00 |0. 00 |1. 05 |1E+30 |0. 272727279 | |X3 |0. 0 |-0. 38 |1. 350000002 |0. 375000011 |1E+30 | | | | | | | | | | | | | | | | |Final |Shadow |Constraint |Allowable |Allowable | |Name |Value |Price |R.
H. Side |Increase |Decrease | |Space Constraint|50625 |0 |55296 |1E+30 |4671 | |Total | | | | | | |Budget |1500 |1. |1500 |158 |1500 | |Constraint | | | | | | |Total | | | | | | |Demand |0 |-0. 375 |0 |2000 |3333. 33333 | |Constraint 1 | | | | | | |Total | | | | | | |Demand |1250 |0 |0 |1250 |1E+30 | |Constraint 2 | | | | | | |Total | | | | | |
Julia can borrow a maximum of 158. 00 to facilitate maximum profit As with all rental booths space is very limited and the money to be borrowed was for additional supplies and food items, therefore the amount of space that these items need are the primary constraint in this case study. C. When Julia looked at the solution in (A), she realized that it would be physically difficult for her to prepare all the hot dogs and barbecue sandwiches indicated in this solution. She believes she can hire a friend of hers to help her for $100. 0 per game. Based on the results in (A) and (B), is this something you think she could reasonably do and should do? Julia needs to hire a friend strictly for food preparation, because the amount of food items that are needed to be sold cannot be prepared by one person even with two people it will be a tight schedule to maintain. However the need for food preparation overrides the cost associated with hiring a friend at 100. 00 per home game. D. Julia seems to be basing her analysis on the assumption that everything will go as she plans..
What are some of the uncertain factors in the model that could go wrong and adversely affect Julia’s analysis? Given these uncertainties and the results in (A), (B), and (C), what do you recommend that Julia do? As with all home games weather plays an important role in the team’s ability to perform well, the same is true for food booth sales, for instance the weather may be too hot for pizza and hotdogs, or it may be too cold for food and the people would rather have hot chocolate.
Not only does weather affect the food types sold it will affect the total amount of fans that are willing to attend the games in general. Therefore weather has the greatest affect on the food sales and Julia’s overall success or failure. For her booth I would recommend adjusting food items based on weather conditions (such as hot chocolate) to offset the losses based on historical data that is affected by weather.