Question

A professor gives two types of quizzes, objective and recall. He is planning to give at least 15

Answer 1

Answer:

x₁ = 20     x₂ = 0

z (min) = 20

Step-by-step explanation:

According to the problem statement:

Let´s call

Objective quiz =  x₁               Recall quiz =  x₂

First constraint

Quantity of quizzes at least 15

x₁  +  x₂  ≥ 15

Second constraint:

Preparation time   at least 300 minutes, then

15*x₁  +  30*x₂  ≥   300

Third constraint

Average score  at least  85 points

7*x₁  +  5*x₂   ≥  85

General constraint x₁ ≥ 0   x₂ ≥ 0

Objective function z is:

z = 1* x₁ + 1,5*x₂     to minimize

The model:

z = x₁  + 1,5x₂      to minimize

Subject to

x₁  +  x₂  ≥ 15

15*x₁  +  30*x₂  ≥   300

7*x₁  +  5*x₂   ≥  85

Using Atozmax (online solver) we find

x₁ = 20     x₂ = 0

z (min) = 20