mathamatics help?

Question

a company makes backpacks.how many backpacks must the company sell to make a profit of more than $250?

nylon pack $3
canvas pack $10

a, write a linear inequality that describes the situation

b, Graph the linear equation (just write the coordinates

c, write three possible solutions to the problem

d, why is "10 nylon packs and 22 canvas packs" NOT a solution

Answer 1

Assuming that these pricing figures account for initial expenses (i.e. the company is making $3 profit on nylon packs and $10 profit on canvas packs), you can set up an inequality with n nylon packs and c canvas packs as such:

3n + 10c > 250

Graphing this is easy - if your x axis is nylon and your y axis is canvas, then:

3n + 10c > 250
3n > 250 - 10c
n > 250/3 - 10c/3

You'd graph that like you would a line, but instead of a solid line use a dashed line to represent the inequality. Finally, shade in the top part of the graph - this represents your allowed solutions.

You can find any combination of solutions now:
--If c = 1, then
n > 250/3 - 10c/3
n > 250/3 - 10/3
n > 80

So for one canvas pack, you'd have to sell 81 or more nylon packs. Likewise for c = 2 and c = 3 - you'd have to sell 77 nylons for 2 canvas packs and 74 nylons for 3 canvas packs.

10 nylons and 22 canvas packs won't work - that'd yield a profit of exactly $250, and the requirement was to have more than $250.