Instructions: Given the following constraints, find the maximum and minimum values for z.
x + 3y < 0
Constraints:
x - y = 0
3x - 7y < 16
Optimization Equation: z = -x + 5y
Maximum Value of z: 0
Minimum Value of z:

The answer is below

Step-by-step explanation:

Given the constraints:

x + 3y≤ 0; x - y ≥ 0 and 3x - 7y ≤ 16.

We have to first plot the constraints using the geogebra online graphing tool. Plotting the constraints gives the solution as:

A(0, 0), B(3, -1) and C(-4, -4).

Next using the optimization equation: z = -x + 5y

At point A(0, 0); z = -0 + 5(0) = 0

At point B(3, -1); z = -3 + 5(-1) = -8

At point C(-4, -4); z = -4 + 5(-4) = -24

Hence the maximum value of Z is 0 and the minimum value of Z is -24.

7! = 7×6×5×4×3×2

3! = 3× 2

as 7! is multiple of 3! because 7! contains 3! that is 3× 2 as factor

so 7! /(3! ) = 7× 6× 5× 4

= 42 × 20

= 840

its b) 840✌✌✌

dhruv⭐

step-by-step explanation:

a cube has 6 sides

the probability of getting 5 on the first cube is 1/6 since only one side of the cube has 5 on it.

there are 3 sides of the cube with even number on it [2,4,6]

therefore the probability of getting even number is 3/6

for both events to happen together, the probability would be

1/6 x 3/6 = 12/36

which simplifies to 1/12