JULIA’S FOOD BOOTH:

Total area: 36*48 = 1728

Let P = Number of Pizza Slices

H = Number of Hot Dogs

B = Number of Barbecue Sandwiches

Individual Area:

Pizza = 154

Hot dog = 16

Barbecue Sandwich - 25

Cost for each:

Pizza: 1.5 – 6/8 =

Hot Dog: 1.5-0.45 =

Barbecue Sandwich: 2.25-0.9 =

FORMULATION:

1. Pizza:

To find area:

Total area: 14*14 = 196 inches square

For each slice: 196/8 = 24 inches per slice

Similarly the given areas for

2. Hot dogs: 16 square inches

3. Barbecue Sandwiches = 25 square inches

Question A: Formulate and solve a linear programming model for Julia that will help you advise

her if she should lease the booth.

Solution : Objective Function:

Maximise Z = $0.75P +$ 1.05 H +$1.35 B

Constraints:

24P + 16H + 25B <= 55,296 square inches

P >= H+B

H >= 2B

and Non- negative constraints : P, B & H >= 0

She makes a profit of $2250. She makes use of : 1000 + 100 = $1100 . Therefore : $2250 -

$1100 = $1150. Therefore, we advise her to lease the booth.

Question 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)?

Solution From the report it can be seen that, the Shadow price for the budget constraint is 1.5

and the allowable increase is 158.88. This means that each dollar added to the budget can

increase a profit of $1.5 and the maximum allowable increase is 158.88. So maximum amount that

Julia can borrow from her friend to make profit is $158.88 and it will make an additional profit of

158.88 x 1.5 = 238.32.

Question 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 per game. Based on the results in

(A) and (B), is this something you think she could reasonably do and should do?

Solution: If Julia hires a friend to help her for $100 per game, her net profit per game will be

1150-100 = $1050. Still, as per her strategy, it is worth leasing the booth. Hence, she should hire

her friend if it is physically difficult for her to prepare the required quantity of hot dogs.

Question 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?

Solution: The main uncertain factor is demand. She believes that she will sell everything she can stock and

develop a customer base for the season. If this is violated, then nothing would work.

As per result in (A), the net profit she can earn is $1150. It is above her target $1000. Hence, she can suffer

a profit of $150/- within her target.

As per result in (B), if she borrows money from her friend of $158.88, she will earn a profit of $1387

( $2487 - $1100) where she will selling 1381 pizza slices and 1381 hot dogs.

Now, as per the result in (C), if she hires for a friend to help her per $100 per game, she will be earning a

profit of $1050 as shown above and the threshold limit for her preparation of hot dogs is 1108, which is the

breakeven. (if she prepares less than 1108, she will be under loss) and we aren’t sure whether she will be

able to prepare 1108 hot dogs by herself. So, it’s better to hire a friend which will help her to make profit.