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Julia Case Problem

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Assignment #3: Case Problem "Julia's Food Booth"

Complete the "Julia's Food Booth" case problem on page 109 of the text. Address each of the issues A - D according the instructions given. (A) Formulate and solve an L.P. model for this case.
There are three products or variables in this problem that we must consider for purchase.

X1 = number of pizza slices Julia should purchase
X2 = number of hotdogs Julia should purchase
X3 = number of barbecue sandwiches Julia should purchase. The reason why Julia is having a booth is to make some money. She wants to maximize her profit that she can get from selling the hotdogs, pizza, and barbeque sandwiches.
The first thing to do is find the profit that Julia will make per Item. To find that per Item price, the cost of the Item will be subtracted from the selling price. Pizza: Julia can buy a pizza that contains 8 slices for 6$. That means each slice of pizza will cost her $0.75. She plans to sell each piece for 1.50.
$1.50-$0.75= $0.75 profit Hot dog:
$1.50 - $0.45 = $1.05 profit Barbecue Sandwiches:
$2.25 - $0.90 = $1.35 profit The objective function can now be written since we have found the potential profit of each food item. The objective of this function is to maximize Z(profit).
Z= $0.75x1 + $1.05x2 + $1.35X3 The Budget is one thing that has to be taken into consideration. Julia has $1,500 on hand to purchase and prepare food for the first home game. A constraint must be formed for the budget. Since the cost of each item and money available is know. It is easy to form the budget constraint. This shows the total cost to purchase each item $0.75X1 + $0.45X2 + $0.90X3.
Since the idea is to remain within the $1,500 budget this is the Budget Constraint:
Budget Constraint $0.75X1 + $0.45X2 + $0.90X3 ≤ 1500 Space is the next constraint that must be…...

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