Crayon packs

Question

A primary school teacher wants to buy new crayons for her class to use on projects. The crayola crayons have 24 crayons per package and each pack costs $3.00. The generic store brand has 42 crayons per package and each package costs $5.00. She can buy at most 8 packages of crayons and can spend no more than $30.00 on all packages. How many of each type of package should she buy to minimize the number of crayons she can provide for her class? What was the maximized number of crayons?

Answer 1

She can buy at most 8 packages , that is the maximum number of packages which implies that the number of students is a multiple of 8

Crayola crayons has 24 crayons per package, and 8 is a factor of 24, thus any number of Crayola crayon package will work for the teacher.

Each package of Crayola crayons costs $3. Within limit of $30 the teacher can by 10 package of Crayola Crayon which will give her 240 crayons in total.

 

Each package of generic brand of crayons comprises 42 crayons. Factors of 42 are 2,3,6 and 7. Thus to satisfy the class of the teacher whose number of students are multiple of 8, at least 4 package of generic brand of crayons needed. 4 packages of generic brand will give 168 crayons and 8 is a factor of 168. 

4 packages of generic crayons @ $5 each package will cost = $20

With remaining $(30-20)=$10 the teacher can buy 3 packages of Crayola crayons.

from 3 packages of crayola crayons she will get 72 crayons and from 4 packages of generic crayons she will get 168 crayons which will give the teacher a total of (168+72)=240 crayons

Anyway, within the cost limit, and without any condition of either cost maximization or cost minimization,  and without conditions of either minimizing or maximizing, the number of packages, she can get minimum and maximum of 240 crayons to provide for the class.

Hence she can either buy 4 package of generic Crayon and 3 package of Crayola crayon or 10 packages  of Crayola crayon.