A professor gives two types of quizzes, objective and recall. He is planning to give at least 15 quizzes this quarter. The student preparation time for an objective quiz is 15 minutes and for a

recall quiz 30 minutes. The professor would like a student to spend at least 5 hours (300 minutes)

preparing for these quizzes above and beyond the normal study time. The average score on an

objective quiz is 7, and on a recall type 5, and the professor would like the students to score at

least 85 points on all quizzes. It takes the professor one minute to grade an objective quiz, and 1.5

minutes to grade a recall type quiz. How many of each type should he give in order to minimize

his grading time?

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

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4