How to write this as an inequality: Across total ticket sales, there cannot be more than three children's tickets sold for every adult ticket sold.

Question

Linear programming

Number of adult tickets sold = x

Number of child tickets sold = y

Total ticket sales is <= 300

Is x<= 3y correct?

Answer 1

y ≤ 3x

In other words, the total number of children's tickets sold (y) is not greater than 3 times the number of adult tickets sold.

If, for example, there were only 3 children's tickets sold, that would need to be less than or equal to 3 times 1 adult ticket sold.

The above inequality is the correct way to express this situation.

Answer 2

Is x<= 3y correct? No this is not right

The condition is for each adult ticket sold at the most 3 children tickets are sold.

In this problem total population of  adult ticket sold can be divided into 4 groups.

Suppose X_i represent a group of adult ticket sold corresponds to Yi number of children ticket sold then

According to condition it is true that Y_i ≤ iX_i where i = 0, 1,2, & 3

                               _{3              3}

Total tickets sold = ∑X_i + ∑ i X_i

                               ^{i=0          i=0}

The linear equality can be generalized to N times at the most

Y_i ≤ iX_i where i = 0, 1,2,3…N and

                               _{N              N}

Total tickets sold = ∑ X_i + ∑ i X_i

                               ^{i=0          i=0}