Question

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Answer 1

Your furniture store sells two types of dining room tables. The first, type A, costs $207, and you make a $29 profit on each one. The second, type B, costs $181, and you make a $19 profit on each one. You can order no more than 190 tables this month, and you need to make at least $4,610 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

Answer 2

let x = # of type A, y = # of type B

type A, costs $207, so x type A tables cost a total of 207x dollars

Answer 3

type B costs 181, so y type B tables cost 181y dollars

Answer 4

total cost: 207x+181y

let c = total cost

this would mean c = 207x+181y

we'll come back to this, but keep it in mind

Answer 5

type A gives you a profit of $29, so x tables of type A brings a total profit of 29x

type B gives you a profit of $19, so x tables of type B brings a total profit of 19y


total profit: 29x + 19y

this must be at least $4,610, so


29x + 19y >= 4610

Answer 6

it further states that

"you must order at least one of each type of table,"

so we know that

x >= 1
y >= 1

Answer 7

these are the choices
90 of type A; 100 of B
111 of type a 79 of B
79 of typr a 111 of type b
100 of type a 90 of type b

Answer 8

oh sry, i didn't see this

"You can order no more than 190 tables this month"

means you also have

x+y <= 190

Answer 9

your next step is to graph the system of inequalities

29x + 19y >= 4610
x+y <= 190
x >= 1
y >= 1

Answer 10

so is it D 100 of type A 90 of B

Answer 11

did you graph the system?

Answer 12

no.. But i was playing with the numbers and came up with this one being the best deal

Answer 13

is it right?

Answer 14

@jim_thompson5910 ??

Answer 15

one sec

Answer 16

ok

Answer 17

you are correct, I just graphed/verified it myself

Answer 18

thanks!!