Question

Jeans costs $15 each and shirts costs $9 each. You have at most $90 to spend clothing. You must purchase at least 3 pairs of jeans. Let x be the amount of jeans purchased and y be the amount of shirts purchased. What is a possible solution?

Answer 1

15x + 9y <= 90

x >= 3

So the jeans themselves cost at least 45$. You have 45$ to spend on anything else as long as it’s less than 90. But you can just use that (3,0) is a solution because you satisfied all the initial conditions with only 3 pairs of jeans

Answer 2

The possible solutions are:

6 jeans and 0 shirts

5 jeans and 0 shirts

5 jeans and 1 shirt

4 jeans and 0 shirt

4 jeans and 1 shirt

4 jeans and 2 shirt

4 jeans and 3 shirt

3 jeans and 0 shirt

3 jeans and 1 shirt

3 jeans and 2 shirt

3 jeans and 3 shirt

3 jeans and 4 shirt

3 jeans and 5 shirt

Explanation:

Cost of 1 jeans=$ 15

and cost of 1 shirt=$ 9

Let x be the amount of jeans purchased and

y be the amount of shirts purchased.

You must purchase at least 3 pairs of jeans.

This means that x ≥ 3---------(1)

The total amount to be spent in shopping is: Atmost $ 90

This means that:

15x+9y ≤ 90------------(2)

From the graph we may see that the solution that lie in the feasible region are labeled in the graph.

( Since, the solution will be where we get the integer value of x and y in the feasible region)