Suppose, due to a improvement in human capital in the Dominican Republic, they are now capable of producing 20 balls in a year, or 50 bats in a year, or any linear combination of those endpoints. ...

Suppose, due to a improvement in human capital in the Dominican Republic, they are now capable of producing 20 balls in a year, or 50 bats in a year, or any linear combination of those endpoints. 

1. if the world wanted to consume 10 bats and as many balls as possible, efficient production could generate a maximum of how many balls? (The answer should be 21.)

2. if the world wanted to consume 15 balls and as many bats as possible, efficient production could generate a maximum of how many bats? (The answer should be 25.)

3. if the world was willing to buy as many units of balls and bats that are produced, but only willing to pay $8 for a ball, $5 for a bat, how many balls and bats will be produced in total?

I don't know how to do these problems.

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

I believe that there is something wrong either with the facts in the question that you asked or with the answers that you have given for #s 1 and 2.  #3 cannot be determined from the information that you have given.

For Questions 1 and 2, it should be relatively simple to find the answers.  This is because we are given two points and we are told that those two points are the endpoints of a line segment.  Given two points, it is possible to find the equation of a line.  First, we have to find the slope of line.  We know that slope is defined as rise/run.  I will say that balls are on the x-axis and bats are on the y-axis. This means that our slope should be the change in the number of bats produced over the change in the number of balls.

The number of bats changes from 0 at one of our points to 50 at the other.  That means the rise of the line is 50.  The number of balls changes from 20 to 0.  That means the run of the line is -20.  So our slope is -50/20 or -5/2.

We are also given the y-intercept of this line.  It is the point where x = 0 which in this case is (0,50). 

If we have the slope and the intercept of the line, we can write the equation in slope-intercept form.  It should be:

Y = -5/2X + 50.

We should then be able to plug in the numbers that you have given in Questions 1 and 2 and get the right answer.  In Question 1, we are told that 10 bats can be produced.  That means the value of y is 10 and we have to solve for x. 

10 = -5/2X + 50

-40 = -5/2X

80 = 5x

X = 16.

So the Dominican Republic can produce 16 balls when it produces 10 bats.  This is not consistent with the answer you were given so something must be wrong.

Similarly, in Question 2 we are told that 15 balls can be produced.  That means the value of x is 15.  If we plug that in to our equation we get

Y = 15(-5/2) + 50

Y = -75/2 + 50

Y = 12.5

So the Dominican Republic can produce 12.5 bats (which we should reduce to 12 since you can’t produce half of a bat) when it produces 15 balls.

From this, we can see that something is wrong.  Either you were given the wrong answers or you have provided the wrong information.  Also, there is no way to know the answer to #3 given the information in this question as we are told nothing about prices in the information given.

Sources:

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