word problems (maximizing profit)

[rachelmaddie]

Hi. I need my work checked please.

let c represent the box of chocolates and k represent the box of cookies

k < 550 + 3c, so k - 3c < 550


k + c < 1950
k - 3c < 550
Multiply the second by 3
k - 3c < 550
3k + 3c < 5850

Add both
4k < 6400
k < 1600 (cookies are less than 1600)

Since cookies yield more than chocolates, to maximize profit they need to sell the maximum amount of cookies.
1599 + 350 = 1949 (less than 1950)

The amount of cookies produced must be no more than 550 boxes plus 3 times the number of chocolate produced.
1599 < 3(350) + 550 = 1050 + 550 = 1600
1599 < 1600
1599 is at least double of 350

350 boxes of chocolates and 1600 cookies for a profit of $5177.5

 

[Deleted member 4993]

Hi. I need my work checked please.
View attachment 20987
let c represent the box of chocolates and k represent the box of cookies

k < 550 + 3c, so k - 3c < 550


k + c < 1950
k - 3c < 550
Multiply the second by 3
k - 3c < 550
3k + 3c < 5850

Add both
4k < 6400
k < 1600 (cookies are less than 1600)

Since cookies yield more than chocolates, to maximize profit they need to sell the maximum amount of cookies.
1599 + 350 = 1949 (less than 1950)

The amount of cookies produced must be no more than 550 boxes plus 3 times the number of chocolate produced.
1599 < 3(350) + 550 = 1050 + 550 = 1600
1599 < 1600
1599 is at least double of 350

350 boxes of chocolates and 1600 cookies for a profit of $5177.5

One problem I see in your work:

Most of the "\(\displaystyle \lt\)" signs should be "\(\displaystyle \le\)"

 

[rachelmaddie]

One problem I see in your work:

Most of the "\(\displaystyle \lt\)" signs should be "\(\displaystyle \le\)"

most of them?

 

[Deleted member 4993]

most of them?

Yes

 

[rachelmaddie]

Yes

Can you please show me ?

 

[Deleted member 4993]

Can you please show me ?

In lines 2-4 (of your answer - how many "<" signs do you have?

How many of those are correct? Which statements in the "problem" support your assertion?