Question

2. The senior class is having a fundraiser to help pay for the senior trip. Selling a box of chocolates yields a profit of $2.45, while selling a box of cookies yields a profit of $2.70. The demand for cookies is at least twice that of chocolates, but the amount of cookies produced must be no more than 550 boxes plus 3 times the number of chocolates produced. Assuming that the senior class can sell every box that they order, how many boxes of each should they order to maximize profit if they cannot order more than 1950 boxes combined?

Answer 1

Answer:

1,600 boxes of cookies and 350 boxes of chocolate

Step-by-step explanation:

cookies: x

chocolate: y

x + y=1950

x $\leq$ 3y + 1550

"amount of cookies produced must be no more than 550 boxes plus 3 times the number of chocolates produced"

so it can be exactly 550 boxes plus 3 times chocolated produced

x $\geq$ 2y

"demand for cookies is at least twice that of chocolates"

so demand for cookies can be exactly 2x for chocolates

plug in graph

two coordinates are:

(1300, 650) and (1600, 350)

equation:

$=2.7x+2.45y

2.7(1300)+2.45(650)=5102.5

2.7(1600)+2.45(350)=5,195.5

1600 boxes of cookies and 350 boxes of chocolates make the most money