Julia’s Food Booth

(A) Formulate and solve an LP model for this case The neutral here is to maximize the pull in. Profit is calculated for each vari able-bodied by subtracting cost 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) gross sales Price 1.50 1.50 2.25 Cost 0.75 0.45 0.90 Profit 0.75 1.05 1.35*For Pizza stroke Cost/Slice = $6/8 = $0.75 cost per slice Maximize Z = 0.75 X1 + 1.05 X2 + 1.35 X3 Constraints budget 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 impart space required for a 14 * 14 pizza = 196 in2. Since in that respect are eight slices, we divide 196 by eight, and this gives us approx. 24 in2 per slice. The constitutional dimension of the oven is the dimension of the oven shelf, 36 in * 48 in = great gross in2, multiplied by 16 shelves = 27,648 in2,which is multiplied by 2, in the first place jump and during the halftime, giving a total space of 55,296 in 2.(B) Evaluate the horizon of fasten oning money before the first hazard. The shadow price or dual value is $1.50 for each additional dollar Julia would enlarge her profit, if she borrows around money. However, the upper limit of the sensitivity range 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 $100/game to assist. Yes, she should hire her friend for $100/game for it is almost impossible for her to cultivate all the food in such a short 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 extra $158.88 she would be able to pay her friend.(D) Analyze the stir of uncertainties on the model.The impact of uncertainties such as weather (to sunny, rainy, or cold), competition, increase in food cost, and the attendance at each of the six games could stifle the demand for the items sold by Julia. If it is raining or cold thus 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 depart change and so does her profit. She will not be able to state a $1000 profit under high uncertainty.