Julia's Food Booth

1.

Let,

x1 = Number of slices of pizza

x2 = Number of hotdogs

x3 = Number of barbeque sandwiches

Maximize Z = .75x1 +1.05x2+1.35x3

Subject to:

1x1 - x2- x3 >= 0

x2 - 2x3 >= 0

.75x1 + .45x2 + .9x3 <= 400

153.94x1 + 16x2 +25 x3 <=27648

x1, x2,x3>= 0

2.

Number of slices of pizza = 160

Number of Hotdogs = 107

Number of Sandwiches = 53

Profit = $ 303.7539031

The profit for Julia will be $303.75 only, which is less than $1000, so Julia should not lease the booth.

3. According to the sensitivity analysis report, if Julia could borrow money from a friend to purchase more ingredients, the profit would be unchanged. This is due to the fact that there is only limited space available for the storage of food items. If she could use the extra money to buy more shelf space she could increase the profit.

4. The sensitivity analysis report from question 1 indicates that out of the $400 Julia had; only $215 was used for buying the ingredients. $184 was unused because of the space constraint. She could not be able to use the left over amount because the shelf space available is limited. If she hires her friend to assist her for $100, the money available to buy the ingredients will be $300. The sensitivity report generated as per the changed constraint indicates that the profit was unchanged because $100 is less than $184, which is the unused amount. So, if the money available is less than $216 (400-184), the profit would be reduced.

5. Julia is confident that she could sell a lot of food during the games because everyone eats a lot of food during games. People might eat a lot of food during the games but, Julia's business will depend upon the competitors. So, before starting the business she should know how strong the competition is. If the competition is tight she might not be able to sell everything she can stock. In that case the sensitivity analysis might be wrong.

Julia thinks that slices of cheese pizza, hotdogs and, barbeque sandwiches are the most popular food items. But, before starting the business she should do a thorough study about this.

Julia should make sure that the food will be ready during the hour before the game and during half time. She should make necessary arrangements to get the pizza on time and if she is not able to prepare the food on time,