Julia is planning to lease a food booth outside the Tech Stadium at Home Football games to finance her last year education with all the games go sold out. The rent for the booth per game is $ 1000. Julia will sell slices of Cheese Pizza, Hot Dogs and Barbecue Sandwiches which are acclaimed to be the most popular so these are the three products she has chosen to sell at the home games football stadium. The rent for oven is $ 600 for six home games, which makes it $ 100 per game. To keep things simple, Julia decided to hire an outside pizza delivery company, it seems to be cost effective and for other items she plans to prepare them the night before. Space taken by Pizza is 14” x 14”, hot dogs are 16 in/sq. and the BBQ sandwich is 25 “sq.
The cost price of Pizza $6.00, or $.75 ea slice with 8 slices/pizza the hot dogs $0.45 each, and sandwiches$.90 each, respectively. The sale price of Pizza Slice is $1.50, hot dogs $1.60 and the BB-Q sandwich is $2.25. Julia’s initial investment is $1500 which would pay for the first game day; she would pay the future home games out of proceeds earned from the games. From Student Feedbacks she has learnt that she can sell as many slices of Pizza as Hot dogs and BBQ sandwich’s combined. She feels she can sell twice as many hot dogs as she can the BBQ sandwich’s. Julia believes that she can make at least $1000 net profit after expenses are paid per game.
Objective here is to maximize the profit. Profit is calculated for each variable by subtracting cost from the selling price. Pizza. Cost $6 / 8 = $ 0.75 (Cost per slice) Z =$0.75 x1 +$.45×2 + $.90 x3. Profit per: $.75/slice pizza, $1.15/hot dog $ 1.35/BBQ Sandwich Sales Price: $2.25 $ 1.60 $ 1.50 Sale Price: 3x/Sandwich; 2x/ Hot dog and 1x/pizza slice.
Decision Variables Constraints:
0.75×1 + 0.45×2 + .90×3 2×3
x2 – 2×3 => 0
If extra help @$100/game = $100/x6
Non Negative Restrictions:
x1, x2 , x3 all are >= 0
Maximize Total Profit:
Z = 0.75×1 + 0.45×2 + .90×3 = 0
D. Over all with the expenses of food supplies, oven leasing, the booth and the pay for help, she will still be far ahead in her net profit and it will be well worth the help in the end. Certainly there will be uncertainty, which is with all endeavors, but those have to be accounted for as best you can.
Taylor, B. W. (2011). Introduction to Management Science. Upper Saddle River, NJ: Prentice Hall. coursehero, (2009, Apr. 13). linear programing [Msg google..com]. Message posted to http://coursehero.com/