Question

Two learners are planning to make baskets to raise money for the honors society at their school. Marcia will make baskets out of palms. Norma plans to make baskets out of pine straw. Together, they have $100 to spend on supplies.The palm baskets cost $4 to make and will sell for $20.The pine straw baskets cost $3 to make and will sell for $17.The learners agree that they will each make at least 14 items. Let x represent the number of palm baskets and let y represent the number of pine straw baskets.Write the objective function for representing the income from the sale of the baskets.Write an inequality to represent the number of palm baskets Marcia will make.Write an inequality to represent the number of palm baskets Marcia will make.

Answer 1

The earnings from the sales of the palm baskest is 20x, where x is the number of palm baskets, the cost of making x palm baskets is 4x. Then, the total income for this kind of baskets is:

20x - 4x = 16x

The earnings from the sales of the pine straw baskest is 17y, where y is the number baskets, the cost of making x pine straw baskets is 3y. Then, the total income for this kind of baskets is:

17y - 3y = 14y

The objective function is:

f(x,y) = 16x + 14y

They have $100 to spend on supplies. Then, based on the costs to make the baskets you can write:

4x + 3y ≤ 100

The learners agree that they will each make at least 14 items. Then, you have:

x + y ≤ 14

By using the previous inequalities, you can solve for x and y as follow:

4x + 3y ≤ 100 solving for x

4x ≤ -3y + 100

x ≤ -3/4 y + 25

x + y ≤ 14 solving for y

y ≤ -x + 14