Taco Quatro can make their entire menu out of their fantastic four Mexican ingredients, cheese, meat, beans and tortillas. A Nacholupa (N) needs 2 ounces of cheese, 4 ounces of beans and 3 tortillas. A Quesatilla (Q) needs 4 ounces of cheese, 2 ounces of meat and 1 tortilla. An Enchinacho (E) requires 2 ounces each of cheese, meat, and beans plus 3 tortillas. Their newest menu item, the Burritaco (B) needs 4 ounces of cheese, 2 ounces of meat and one tortilla. A Nacholupa sells for $2.75, a Quesatilla sells for $2, an Enchinacho sells for $3 and the new Burritaco sells for $4. The assistant manager checks the cooler one fine Monday morning and sees that they have 400 ounces of cheese, 150 ounces of meat, 400 ounces of beans and 250 tortillas on hand. Then how many units of each product should be produced to maximize the revenue

The solution is:

z (max ) =  446.25 $

x₁  =  55     x₂  =  0    x₃  = 5     x₄  =  70  

Step-by-step explanation:

From problem statement:

                     Nacholupa       Quesatilla      Enchinacho    Burritaco

                           x₁                        x₂                     x₃                   x₄

Cheese               2                         4                      2                    4

meat                   0                          2                     2                     2

beans                  4                         0                      2                     0

Tortillas               3                          1                      3                     1

Price $               2.75                      2                      3                     4

From table :

    z =   2.75*x₁  + 2*x₂  + 3*x₃  + 4*x₄   to maximize

Subject to:

Availability of cheese: 400 ou

2*x₁  +  4*x₂  +  2*x₃  +  4*x₄  ≤ 400

Availability of meat  :  150 ou

             2*x₂  +  2*x₃  +  2*x₄ ≤  150

Availability of beans :  400 ou

   4*x₁             + 2*x₃               ≤  400

Availability of tortillas :   250

3*x₁  +  x₂   +  3*x₃  +  x₄   ≤ 250

General constraints:

x₁ ≥  0             x₂  ≥  0              x₃  ≥  0              x₄  ≥ 0

All integers

With the use of AtomZmath  ( integer solving on-line software )

The solution is:

z (max ) =  446.25 $

x₁  =  55     x₂  =  0    x₃  = 5     x₄  =  70  

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

  q

step-by-step explanation:

each line from a vertex to the midpoint of the opposite side is called a median. the point where the medians intersect, point q, is the centroid.

the centroid of δabc is point q.