. Model Problem
Coffee vs. Tea
A café by Lindsay's house sells coffee and tea. They are trying to make the most amount of money
possible. In other words they are trying to maximize profit. They asked me to look at their sales
receipts and figure out what they should do. But they had a few limitations on what could be done.
Constraint #1: The Baristas (the people who makes the coffee) can only reasonably serve 90 cups
per shift. It can be 90 cups of coffee, 90 cups of tea or a mixture of the two.
Constraint #2: Coffee costs $3 per cup and Tea costs $2. In order to stay on track to pay their
bills, the owners would like to sell at least $120 worth of beverages every shift.
Constraint #3: They have a limited supply of coffee and tea that gets delivered every day. If they
don't want to sell out (And annoy customers) they can sell no more than 70 cups of tea per shift.
Constraint #4: Similar to the last constraint, they can only sell 60 cups of coffee per shift before
they sell out.
Question: How much tea and how much coffee should they sell every shift in order to maximize
profits? They make $1.10 on each cup of coffee and $.90 on each cup of tea.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

im pretty sure it would be 5 am, hope that , and give brainliest and guys if this is right then press the button and give 5 stars

with btw u said 100pts but it clearly says

i answerd and just got 10pts

no hate

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights