Julie’s Food Booth Case Study

Julie’s Food Booth Case Study

Introduction

Julia Food Booth is a sole proprietorship business that Julia is consider opening as an option to finance her final year at school. The business is to be operated during football matches in a stadium booth. The management of the stadium only allows anyone operating the booths to sell fast food or drinks, but not both. Currently, Julia has $1500 for the purchase of food to sell in the booth. The linear problem that can be formulated for Julia is profit maximization. Therefore, for the conditions given in the case study, the paper is divided into five sections, introduction, part A (formulation of linear program and solution), part B (borrowing consideration), part C (hiring), and part D (uncertainties).

Part A

The conditions for Julia’s food booth are: the food items to sell are: Cheese pizza, Hot dog, and Barbecue sandwiches. The booth costs $1000 per game, and the Oven cost $6000 for 6-home games pers season, implying that it cost $1000 per game. The oven is made up of 16 selves each 3 x 4 feet in space. This can be converted to inches as follows (1 foot = 12 inches):

This implies that Julia has a total space of 10,368 squared inches to stock her booth with food. A piece of pizza occupies 14 squared inches and contains eight slices. The cost of one piece of pizza is $6 while it sells for $1.5 per slice. This means that the cost per slice is , giving a profit of  per slice. However, we need a profit per square inches. The number of slices from one squared foot of pizza is . Thus, profit per square inch is  per square inch of pizza. Now, let the number of squared feet of pizza Julia order per game be . Next, 16 sq. Inch of hot dog cost $0.45and sells at $1.5, meaning 16 sq. Inch of the hot dog gives a profit of . However, one squared foot of hot dog gives a profit of . Then, let the number of squared feet of hot dog Julia order per game be . Similarly, 25 sq. Inch of barbecue cost $0.90 and sells at $2.25, meaning 25 sq. Inch of the hot dog gives a profit of 2.2. However, one squared foot of barbecue gives a profit of . Then, let the number of squared feet of barbecue Julia prepare per game be..

The objective of Julia is to maximize profit = profit from food – fixed cost

Fixed cost = Booth + Oven = 1000 + 1000 = $ 2000.

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However, the following constraints must be taken into consideration:

The total squared feet of food must not exceed the oven space.

The cost of purchasing or making the food item should not exceed available cash of $1500

She should sell at least twice as many hot dogs as barbecue sandwiches

which simplifies to

From the experience of other business people accounts, Julie anticipates selling more slices of pizza as a combined total of hot dog and barbecue.

Finally, Julia cannot stock negative squared feet of any of the three food items

.

Therefore, the linear programs for Julia’s Food Booth is

Maximize profit:      } Objective function

Subject to:                 } Oven constraint

} Hot dog and barbecue constraint

} Pizza sales constraint

} cost constraint

} Non-negativity constraint

From excel analysis, the optimal square feet of cheese pizza to order from the local pizza company is 2187.5 sq. Inch approximately 157 pieces of 14 sq. Inch pizza. Similarly, the excel solver shows that Julie should order or make 20,000 sq. Inch of hot dog for each football match, which is approximately 1250 pieces of 16 sq. Inch hot dogs. However, according to the solution of the LP, she should not make any of the barbecue sandwiches. By doing this, she gets a maximum profit of $250. The minimum profit required by Julia in order for her to book the booth is $1000, but the analysis shows that she can only make $250 based on the constraints she has. Therefore, she should consider some of the constraints like the cost of pizza, hot dogs, and sandwiches.

Part B

The decision in this part is based on the sensitivity report from excel (Dale, 2013; Fayad, 2019; Gaweda, 2018). In the constraint cells, the amount that Julie can borrow from the friend is $369.16. This means she will have $1869.16 for the purchase of the ingredients and order the pizzas. With this new value, the maximum profit from the business would be $803.74, as shown in the second set of analyses performed in excel. Thus, the additional profit from the borrowed cash would be $803.74 – $250 = $553.74 per game. The shadow price of 1.5 from the first LP sensitivity results shows that if the additional cash exceeds $369.16, then the maximum profit will decrease instead of increasing. Therefore, the main constraint is the available space in the oven.

Part C

From part A the number of hot dogs to make is 1250 of 16 sq. Inch each this is a heavy task for one person; thus, she should consider hiring a friend for $100. From part B, she can still cash in a profit of $803.74 – $100 = $703.74 in every game. Therefore, given the profit margin and the amount of work she will perform, she should higher the friend for making the 1250 hot dogs.

Part D

The uncertainties that she should take into account are:

• Low demand for any or all of the products. This will imply that not all of the products will be sold and she will have to factor that in her losses (costs).
• Delay from the local pizza company; the 157 pizzas might delay, yet she is operating on a fixed schedule of sales (one hour before the match and during the half time). This uncertainty will imply that the customers will demand a product that she does not have. Thus, paying the fixed cost for oven and booth but with reduced revenue.
• The friend might charge her interest, thus reducing the profit margin further.
• Adverse weather condition is one of the main causes of match postponement, yet Julia makes her hot dogs the previous night, thus postponed match is a direct loss.

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References

Dale, C. S. (2013). Sensitivity report in Excel [YouTube Video]. In YouTube. https://www.youtube.com/watch?v=1lQQRMMzsno

Fayad. (2019). Shadow price excel solver Linear programming [YouTube Video]. In YouTube. https://www.youtube.com/watch?v=vXTef5-b1pY

Gaweda, A. (2018). Understanding Excel’s Sensitivity Report [YouTube Video]. In YouTube. https://www.youtube.com/watch?v=kdL3fkbx2sE&pbjreload=10