Question

Problem #1 Gabriela operates a taco stand and can make Beef Tacos (BT) and Veggie Especials (VE). A Beef Taco sells for $3 and takes 1 tortilla, 1 cup beef and 0.5 cups each of beans and cheese. A Veggie Especial sells for $2.00 and takes 1 tortilla and 1 cup each of beans and cheese. Today, Gabriela is down to her last few supplies: 10 tortillas, 8 cups of beans, 7 cups of cheese and 8 cups of ground beef. She wanted to use a graphical LP to maximize her revenue, but ran out of time- she's drawn in her constraints related to materials, but she has not been able to label them nor add the fact she has an existing order for 1 Veggie Especial. She also hasn't colored in the feasible region or written an objective function. Finish her work please: (2 points) define and formulate variables (4 points) formulate, plot and label constraints (2 points) accurately and clearly shade the feasible region (2 points) write an objective function, are we maximizing or minimizing? ...and answer more of the questions below 18 16 14 12 10 tortillas beans 一cheese 8 ground beef 0 2 4 6 8 10 12 14 16 18 20 22 Veggie Especial (VE) (2 points) How much at the most can Gabriela make today? (2 points) ldentify redundant constraints? (2 points) What type of constraint is the existing Veggie Especial? (4 points) She was able to borrow 2 tortillas from another vendor. How does that change her revenue? (5 points) It turns out Gabriela also has a pre-existing order for 2 beef tacos. How does that change your optimal solution and revenue?

Please show work so I can understand it!! Thank you!!

Answer 1

Let X1 = # of veggie especial and X2 = # of beef tacos

Formulation

Maximize 2X1 + 3X2

S.T

X1 + X1 <= 10

X1 + 0.5X2 <= 8

X1 + 0.5X2 <= 7

X2 <= 8

X1, X2 >= 0

The labels are shown below (marked on the same image). The constraint lines and equations are color coded. The feasible region is marked in white.

..and answer more of the questions below 18 φ x1 +10.532< 8 16 141) x1 + 0.5x2 <= 7 : 12 ーtortillas 10 beans Cheese ground beef x2<= 8 0 2 4 6 8 10 12 14 16 18 20 22 Veggie Especial (VE)

The objective function is maximizing and it is written above.

The maximum value is obtained at the point where X2 = 8 and X1 + X2 = 10 intersects. That is (2,8)

This means Gabriela can make maximum of 2 Veggie Especial and 8 Tacos and maximize her profit to 28.

The redundant constraint is X1 + 0.5X2 <= 8 and X1 + 0.5X2 <= 7

Existing veggie especial is a non-zero/integer constraint

If she had 12 tortillas, then her line X1 + X2 = 10 will shift to 12 and this means the point will be modified to (3,8). This means the total revenue will be 30

In the original optimal solution we have X2 = 8. This clearly surpasses the value of X2 >= 2. This means the optimal solution will not change