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avatar+104 

1) All sacks of sugar have the same weight. All sacks of flour also have the same weight, but not necessarily the same as the weight of the sacks of sugar. Suppose that two sacks of sugar together with three sacks of flour weigh no more than 40 pounds and that the weight of a sack of flour is no more than 5 pounds more than the weight of two sacks of sugar. What is the largest possible weight (in pounds) of a sack of flour?

 

2) The Highly Improbable Foods Company makes vegetarian versions of burgers, hot dogs, and chicken wings, and they offer two platters. Platter A consists of one burger, three hot dogs, and 5 chicken wings, which costs $16. Platter B consists of two burgers, one hot dog, and 8 chicken wings, which costs $20.

A picnic organizer requires 80 hamburgers, 95 hot dogs, and 380 chicken wings. (There can be leftovers, but these are the minimum requirements.) What is the minimum cost (in dollars)?

 Mar 19, 2020
 #1
avatar+1956 
+3

1) The same question was posted here: https://web2.0calc.com/questions/help_55674

 

2) 

Let x and y represent the numbers of Platter A and Platter B the organizer needs to purchase.. 

  x + 2y ≥ 80.  80+ hamburgers are required

  3x + y ≥ 95 . 95+hot dogs are required

  5x +8y ≥ 380.38+ chicken wings are required

  16x +20y = c 

 

The vertex is (x, y) = (20, 35). The other vertex close to the origin is (60, 10). The cost of that order would be $1310.

The value of an order of 20 Platter A and 35 Platter B is $1020

 Mar 19, 2020
edited by CalTheGreat  Mar 19, 2020
edited by CalTheGreat  Mar 19, 2020
 #2
avatar+104 
0

thanks for #2! that cleared things up. for #1.. it's a similar problem but the numbers are different. 

 Mar 19, 2020
 #3
avatar+1956 
+2

Woops! Sorry. I will post the answer to number 1 soon.

 Mar 19, 2020
 #4
avatar+1956 
+1

Here's a hint for #1.

 

We can create inequalities like this:

 

3x+4y ≤ 40

2y-3x ≤5

 

To solve this problem, try to get y to the biggest possible value. Hope this helped!!!

 Mar 19, 2020
 #5
avatar+104 
0

wait- what do the variables represent?

matthewmacdell  Mar 19, 2020
 #6
avatar+1956 
+1

Oh wow I forgot the basics...LOL!

 

 weight of a sack of sugar  =  x

weight of a sack of flour  = y

 Mar 19, 2020
 #7
avatar+111321 
+1

1) All sacks of sugar have the same weight. All sacks of flour also have the same weight, but not necessarily the same as the weight of the sacks of sugar. Suppose that two sacks of sugar together with three sacks of flour weigh no more than 40 pounds and that the weight of a sack of flour is no more than 5 pounds more than the weight of two sacks of sugar. What is the largest possible weight (in pounds) of a sack of flour?

 

I solve this with linear programming  (and a little Agebra)

 

Let x  = weight of sack of sugar

Let y = weight of a sck of flour

 

We  have these inequalities

 

2x + 3y  ≤ 40

y - 2x ≤  5

 

Set  these up as  equalities

 

2x + 3y  = 40      (1) 

y  -2x   =  5       ⇒   y = 5 + 2x     (2)

 

Sub (2) into (1)   and we have that

 

2x +3( 5 + 2x) =  40

8x + 15  = 40

8x = 25

x = 25/8   =   3.125 lbs  

 

So...max weight for a sack of flour  = 5 + 2(3.125)  =  11.25 lbs  

 

See the graph here : https://www.desmos.com/calculator/pjcr7qcxiz

 

The max for the weight of a sack of flour occurs at (3.125, 11.25)

 

 

cool cool cool

 Mar 19, 2020

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