Julia’s Food Booth

(A) Formulate and solve an LP simulation for this case The objective here is to maximize the net profit. Profit is calculated for each variable by subtracting equal from the selling price. The decision variables used are X1 for pizza slices, X2 for hotdog, and X3 for BBQ sandwich.X1 (pizza) X2 (hotdog) X3 (sandwich) Sales Price 1.50 1.50 2.25 Cost 0.75 0.45 0.90 Profit 0.75 1.05 1.35*For pizza pie Slice Cost/Slice = $6/8 = $0.75 cost per slice Maximize Z = 0.75 X1 + 1.05 X2 + 1.35 X3 Constraints cipher 0.75X1 + 0.45X2 + 0.90X3 1500 Oven Space 24X1 + 16X2 + 25X3 55,296 in2 The calculation for the oven space is as follows Pizza slice total space required for a 14 * 14 pizza = 196 in2. Since there are eight slices, we divide 196 by eight, and this gives us approx. 24 in2 per slice. The total dimension of the oven is the dimension of the oven shelf, 36 in * 48 in = 1728 in2, multiplied by 16 shelves = 27,648 in2,which is multiplied by 2, forward kickoff and during the halftime, g iving a total space of 55,296 in 2.(B) Evaluate the prospect of borrowing money before the first game. The shadow price or triplex value is $1.50 for each additional dollar Julia would increase her profit, if she borrows some money. However, the upper limit of the sensitivity puke is $1,658.88, so she should only borrow $158.77 and her additional profit would be $238.32 or a total profit of $2488.32.(C) Evaluate the prospect of paying a friend $century/game to assist. Yes, she should hire her friend for $100/game for it is almost impossible for her to prepare all the food in such a compendious time. In order for Julia to prepare the hotdogs and barbeque sandwiches she would need the additional help. With Julia being able to borrow the tautological $158.88 she would be able to pay her friend.(D) Analyze the impact of uncertainties on the model.The impact of uncertainties such as brave (to sunny, rainy, or cold), competition, increase in food cost, and the attendance at each of t he six games could reduce the necessary for the items sold by Julia. If it is raining or cold then there may not be as many patrons at the games and if it is to hot people may not want to eat before or during the games. The higher the uncertainties the demand shifts, therefore the solution of the LP model go away change and so does her profit. She will not be able to produce a $1000 profit under high uncertainty.