Question

Christine’s Butter Cookies sells large and small tins of cookies. The factory can prepare at most 200 tins of cookies each day. Each large tin requires 2 pounds of butter. Each small tin requires one pound of butter. Only 300 lbs. of butter is available daily.

The profit from each day’s cookie production is estimated by the function, f(x,y) = $6.00x + $4.80y, where x is the number of large tins sold and y is the number of small tins sold. What is the maximum profit that Christine’s Butter Cookies can expect in a day?

Answer 1

We also have 2x+y=300 since "each large tin requires 2 pounds ...."

Answer 2

y=300-2x

Answer 3

and \[x+y \le 200\] because of "the factory can prepare at most 200 tins of cookies each day"

Answer 4

possible answers:

$920

$1080

$600

$480

Answer 5

f(x,y)=6x+4.8y=6x+4.8(300-2x)=1440-3.6x

Answer 6

So when x=0 the profit would be the greatest

Answer 7

But x cannot be 0 or otherwise y would be 300

Answer 8

So we minimize the x

Answer 9

And you'd get x=100

Answer 10

Plug it back into 1440-3.6x

Answer 11

And you should get the answer

Answer 12

that isn't right, it would be 80

Answer 13

What would be 80?

Answer 14

1440-3.6*100 doesn't seem to be 80?

Answer 15

oh just kidding. i didn't type it correctly. it is 1080. that is right then.

Answer 16

Do you understand why x=100?

Answer 17

2x+y=300
x+y=200

Answer 18

oh, okay. I get it. Thank you @kc_kennylau

Answer 19

no problem