Word Problems

1
Word Problems 1) Find objective function 2)
Find constraints 3) Graph feasible region 4)
Find vertices 5) Answer question
Page 166 8 From the book. Your club plans to
raise money by selling two sizes of fruit
baskets. The plan is to buy small baskets for
10 and sell them for 16, and to buy large
baskets for 15 and sell them for 25. The club
president estimates that you will not sell more
than 100 baskets. Your club can afford to spend
up to 1200 to buy baskets. Find the number of
small and large fruit baskets you should buy in
order to maximize profit.
-10(x y 100) 10x 15y 1200 -10x 10y
-1000 10x 15y 1200 5y 200 y 40, x 60
x ? Small baskets, y ? Large baskets
x 0, y 100 x 100, y 0
x 0, y 80 x 120, y 0
80 large baskets, make 800 dollars.
P 6x 10y
6(0) 10(80) 800
x y 100
0 0 100 True
0 0 1200 True
(0, 80)
10x 15y 1200
6(60) 10(40) 760
x 0 y 0
(60, 40)
0
You want to maximize profit. Small baskets, buy
for 10, sell for 16, profit is 6. Large
baskets, buy for 15, sell for 25, profit is 10
Total amount of baskets has to be less than or
equal to 100.
The total amount to spend to buy stuff is 1200.
It costs 10 for the small basket, and 15 to buy
the big basket.
Remember, cant have negative baskets
Need to find the intersection of the red and
green line. I will use linear combination method.
Remember, plug each vertex into the objective
function to find max and min. Then answer the
question.
(0, 0)
6(100) 10(0) 600
10
(100, 0)