Question

-Naomi and her children went into a bakery where they sell donuts for $1.25 each and cookies for $0.75 cach. Naomi has $15 to spend and must buy at least 14 donuts and cookies altogether. Also, she must buy a minimum of 2 donuts. If o represents the number of donuts purchased and y represents the number of cookies purchased, write and solve a system of inequalities graphically and determine one possible solution.​

Answer 1

A possible solution that satisfies all the conditions, obtained from the graph of the inequalities is Naomi buys o = 9 donuts and y = 5 cookies

Please find attached, the graph of the system of inequalities, showing the feasible region which are the solutions of the inequalities, created with MS Excel

The number of donuts, o, and cookies, y, Naomi can buy can be calculated as follows;

The number of donuts purchased at the bakery is represented by o, and the number of cookies purchased is represented by y

The details of the question and the parameters indicates that we get the following system of inequalities;

1.25·o + 0.75·y = 15

o + y ≥ 14

o ≥ 2

Please find attached the graph of the system of inequalities, created with MS Excel

The points on the feasible region indicates that the possible solutions are; (9, 5), (2, 112), (2, 16)

Therefore, a possible solution is when she buys 9 donuts and 5 cookies