// fruit company delivers its fruit in two types of boxes: large and small. a delivery of 3 large boxes and 5 small boxes has a total weight of 86 kilograms. a delivery of 6 large boxes and 2 small boxes has a total weight of 122 kilograms. how much does each type of box weigh?

small: 6.25

large: 18.25

Step-by-step explanation:

Set the large boxes as x and the small boxes as y (The weight is the constant).

3x+5y=86

6x+2y=122

Now just solve the systems of equations using either substitution or elimination.

-6x-10y=-172 multiply the whole equation by -2 to eliminate

6x+2y=122, add the equations

-8y=-50

y= 6.25

Plug in y either equation:

3x+5(6.25)=86

3x=86-31.25

3x=54.75

x=18.25

Each small box weighs 6.25 kilograms, each large box weighs 18.25 kilograms, to check plug in the values to the other equation to see if they add up correctly.

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints