Question

The algebra quiz consists of computation

Answer 1

Answer:

To get the highest scores, one needs to answer 4 computational problems and 8 graphical problems.

Step-by-step explanation:

Let x be the required number of computational problems one can answer

And y be the number of graphical problems one can answer.

- One cannot answer more than 12 questions in total

x + y ≤ 12

- Computational problems take 2 mins to answer and graphical problems take 4 mins to answer and there is a maximum of 40 mins for the quiz

2x + 4y ≤ 40

- Then finally, there 6 points associated with a computational problem and 10 points associated with a graphical problem and we want to maximize the number of points obtained from the test.

P(x,y) = 6x + 10y

So, the problem looks more like a linear programming problem to maximize

P(x,y) = 6x + 10y

subject to the constraints

x + y ≤ 12

2x + 4y ≤ 40

solving the constraint equations using the maximum values of the inequalities

x + y = 12

2x + 4y = 40

From the first eqn, x = 12 - y

Substituting into the second wan

2(12 - y) + 4y = 40

24 - 2y + 4y = 40

2y = 16

y = 8

x = 12 - y = 12 - 8 = 4

So, the solution of the equation of constraints, or even the graph of both constraint equation is

x = 4, y = 8

These represents the number of computational and graphical problems to maximally satisfy the constraints and maximize the required number of points.

Hope this Helps!!!