Question

Your furniture store sells two types of dining room tables. The first, type A, costs $265 and you make a $25 profit on each one. The second, type B, costs $100 and you make a $13 profit on each one. You can order no more than 40 tables this month, and you need to make at least $760 profit on them. If you must order at least one of each type of table, how many of each type of table should you order if you want to minimize your cost?

20 of type A; 20 of type B
2 of type A; 38 of type B
30 of type A; and 10 of type B
38 of type A; 2 of type B

Answer 1

a+b ≤ 20

C(a,b)=265a+100b

25a+13b ≥ 760


a+b ≤ 20
25a+13b ≥ 760

25a+25b ≤ 500
25a+13b ≥ 760


25a ≤ 500 - 25b
25a ≥ 760 - 13b

25a ≤ 25a

760 - 13b ≤ 500 - 25b


25b - 13b ≤ 500 - 760
12b ≤ -260
b ≤ -260/12
b ≤ -21.6

Answer 2

A + B ≤ 40

Answer 3

How did you get that ?

Answer 4

" You can order no more than 40 tables this month,"

Answer 5

is this rite for the next step ?

Answer 6

C(a,b)=265a+100b
C(40,-21.6)=265(40)+100(-21.6)=8440

Answer 7

ok . . .

Answer 8

A + B ≤ 40
-> 25 A + 13 ( 40 - A) ≥ 760
=> A ≥ ( 760 - 520 ) / 12 = 20 tables

Answer 9

wow , im sooo confused .

Answer 10

-> B ≤ 20 tables
Thus C ( A, B) = 265* 20 + 100 * 20 = $ 7,300

Answer 11

So , its the 1st answer ?

Answer 12

All I see is one question, minimize cost?

Answer 13

What ?

Answer 14

" how many of each type of table should you order if you want to minimize your cost?

Answer 15

Yeah , and is it the first answer ?
20 of type A; 20 of type B

Answer 16

I guess that's all !

Answer 17

Well , thank you . you helped alot ! I appreciate it (:

Answer 18

Did you see how I solve the equation, make it short it'll be easier to double check!

Answer 19

Yeah , pretty much ! (: