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Julias Food Booth

In: Business and Management

Submitted By mrwinter30
Words 1169
Pages 5
Julia’s Food Booth
Kenneth W. Dayton
Strayer University
11/25/2011
Math 540 Quantitative Reasoning

Julia Robertson is a senior at Tech University and wants to find a way to make extra money to finance her final year at school. She is considering leasing a food booth outside the Tech stadium during home football games. Julia knows the games sell out and the crowd eats a lot of food. Julia has spoken with Ken a consultant and has agreed to investigate her leasing a food booth. Ken will look at the following items to determine if it is a good decision. The first item is creating an L.P. model (linear progression) to help understand the constraints and how to maximize her profit. Julia was asking if she should borrow money from a friend so this will also be evaluated. Julia wants to hire friend to help her with the booth and she is uncertain about the impact of the model. By looking at the L.P. model Ken can determine her best course of action and if she should lease the booth.
The first step is to create the L.P. model to determine an objective function. The objective function ken determines to use is Max Z= .75p+1.05h+1.35b which can be done by looking at the information available such as items being sold, how much those items cost Julia to buy, how much she plans to sell each item for, looking at how one item can sell as much as or more than another item. Julia wants to sell Pizza, Hot Dogs, and Bar-B-Q sandwiches. Julia is going to have a Pizza company deliver a 14 inch Pizza twice each game which will cost her $6.00, Julia estimates it will cost her $0.45 per Hot Dog, and $0.90 for each Bar-B-Q sandwich. Julia plans to sell a piece of Pizza and a Hot Dog for a $1.50 a piece and a sandwich for $2.50. Julia also has to lease a warming oven for the food items; this warming oven has 16 shelves and measure 3x4 each. Julia has $1500.00 in cash to purchase and prepare the food items for the first game and $1000 to lease her booth and Julia would like to clear at least $1000.00 each game (taylor, 2011). Now that Ken has the information needed he can create the L.P. model. (Please see reference 1) Ref.#1Julia's Food Both | | | | | | | | | | | | | | | Products | | Pizza | Hot Dog | BBQ | | Z VALUE | | Profit per unit | 0.75 | 1.05 | 1.35 | | 2250.00 | | Resources | | | | Available | Usage | Remaining | shelf space | | 24.00 | 16.00 | 25.00 | 55296.00 | 50000.00 | 5296.00 | budget | | 0.75 | 0.45 | 0.90 | 1500.00 | 1500.00 | 0.00 | demand | | 1.00 | -1.00 | -1.00 | 0.00 | 0.00 | 0.00 | demand | | 0.00 | 1.00 | -2.00 | 0.00 | 1250.00 | -1250.00 | | | | | | | | | Production | | | | | | | | ANSWER | 1250.00 | 1250.00 | 0.00 | | | | | | | | | | | | | | Max Z= .75p+1.05h+1.35b | | | | | shelve space | 24s+16s+25s greater than or = to 55296.00 | | | | budget | 0.75b+0.45b+.90b greater than or = to 1500 | | | demand | x1 is less than or = to x2+x3 | | | | | demand | x2/x3 less than or = to 2.0 | | | | | | x1,x2,x3 is less than or = to 0 | | | |
By reviewing this L.P. model I is possible to see that Julia stands to make a profit of $2250.00 for the first game. Julia’s lease is $1000.00 per game for her booth so if she subtracts her leasing cost from her profits she is left with a profit of $1250.00 and even with her cost of $100.00 to lease a warming oven she still stands to make a profit. Therefore, Ken recommended it would be ok for Julia to lease a booth.
The next question posed to Ken was in regards to the warming oven ken needed to decide how much space would be needed. Ken did this by dividing the total space required by a pizza per slice (14x14=196in2x8) or 24” per slice. The total space available is per shelf which is 3”x4”. This can be found by multiplying 3*4*144*16*2 which would after calculating the math would be (55296 in2).
The next question Julia asked Ken was if she should borrow more money before the first game? By reviewing the sensitivity analysis report from the above ref.1 the shadow price is $1.50 for each additional dollar therefore, if she were to borrow $158 before the first game she would make an extra profit of $238.32 or a total profit of $2488.32. This answer was found by multiplying t shadow price of 1.50*$158.88 which equals $238.32. Ken found the total profit by multiplying total profit which was $2250.00 and added the additional shadow price which was $238.32. (2250+238.32=2488.32). Please see attached ref. #2 (Ref.#2) | | | | | | | | | Final | Reduced | Objective | Allowable | Allowable | Cell | Name | Value | Cost | Coefficient | Increase | Decrease | $C$12 | ANSWER Pizza | 1250.00 | 0.00 | 0.75 | 1 | 1 | $D$12 | ANSWER Hot Dog | 1250.00 | 0.00 | 1.05 | 1E+30 | 0.272727273 | $E$12 | ANSWER BBQ | 0.00 | -0.37 | 1.35 | 0.375 | 1E+30 | | | | | | | | | | | | | | | | | Final | Shadow | Constraint | Allowable | Allowable | Cell | Name | Value | Price | R.H. Side | Increase | Decrease | $G$6 | shelf space Usage | 50000.00 | 0.00 | 55296 | 1E+30 | 5296 | $G$7 | budget Usage | 1500.00 | 1.50 | 1500 | 158.88 | 1500 | $G$8 | ratio 1 Usage | 0.00 | -0.37 | 0 | 2000 | 3333.333333 | $G$9 | ratio 2 Usage | 1250.00 | 0.00 | 0 | 1250 | 1E+30 | The next question needing an answer was if Julia should hire a friend to assist her with the preparations? Ken reviewed the L.P. model and looked at the profits she would make and since it would be very difficult to prepare the food herself, Ken recommended it would be a good choice to hire her friend for $100.00. Julia would cover the cost out of the additional money she borrowed and that would cover the cost. The last question Julia asked Ken to look at was any uncertainties. Being that the football games take place outside Tech Stadium, one uncertainty is the weather. If the weather is bad less people would come out to the game and less people would eat food. Ken evaluated the L.P. model again and told Julia your chance of reaching a goal of 1000.00 is based on information from the L.P. model with everything going right. Ken also told her that there was little room to play with her profit margin. Ken also explained that if bad weather strikes at any of her games she will not likely make a profit.

References taylor, B. (2011). introduction to management science. (custom ed., Vol. 2011, p. 109). upper saddle, NJ: Pearson.

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