Use the technique developed in this section to solve the minimization problem. Minimize C = −3x − 2y − z subject to −x + 2y − z ≤ 20 x − 2y + 2z ≤ 25 2x + 4y − 3z ≤ 30 x ≥ 0, y ≥ 0, z ≥ 0 The minimum is C = at (x, y, z) = .

C= -145, (35/4, 295/8, 45)

Step-by-step explanation:

Use Gaussian elimination to find the values of x, y and z

Eq 1: -x+2y-z=20

Eq 2: x-2y+2z=25

Eq 3: 2x+4y-3z=30

Eq 1: (-x+2y-z=20 ) × 1

Eq 2:  x-2y+2z=25

Eq 3:  2x+4y-3z=30

⇒ Eq1: -x+2y-z=20

    Eq2:         z= 45

   Eq 3: 2x+4y-3z=30

Eq1:  (-x+2y-z=20 ) × 2

Eq2:            z= 45

Eq3:   2x+4y-3z=30

⇒ Eq1:  -x+2y-z=20

   Eq2:            z= 45

  Eq3:      8y-5z= 70

Eq 1: -x+2y-z=20

Eq 3:     8y-5z= 70

Eq 2:       z= 45

Z=45

y= 295/8

x= 35/4

C= -145

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: