Question

Production Planning. A manufacturer builds racing bikes and mountain bikes, with the per unit manufacturing costs shown in the table. The company has budgeted 26,150 for materials and 31,800 for labor. How many bikes of each type can be built?
materials labor
racing 110 120
mountain 140 180

Answer 1

Hey :)

Answer 2

you will make X racing bikes and Y mountain bikes.

Answer 3

hi :)

Answer 4

yes, this is where im confused, most of my other problems i pair a number with x and a number with y

Answer 5

so for each racing bike you will use110 materials and 120 labor, right?

Answer 6

meaning being, for X number of racing bikes, you will use 110 * X materials and 120 * X labor.

Answer 7

so 110x + 120y = ??

Answer 8

140x+180y = ??

Answer 9

no nono

Answer 10

it's going to be 110x and 120x

Answer 11

but you won't get anything from that.

Answer 12

read this again. "meaning being, for X number of racing bikes, you will use 110 * X materials and 120 * X labor."

Answer 13

ok so for each racing bike(X) i will charge 230

Answer 14

haha, noo...

Answer 15

sorry, i was talking somewhere else. i'm done with that now. let me finish my sentence

Answer 16

ok for Mountain bikes, Y amount of mountain bikes is going to cost you 140y of materials and 180y of labor.

Answer 17

now lets look back at the question. we have total of 26150 labor.

Answer 18

110x + 140y = 26150?

Answer 19

YES!

Answer 20

and for the labor?

Answer 21

120x+180y=31800

Answer 22

but how do i eliminate those

Answer 23

now its just algebra

Answer 24

to make things easier, lets divide each side by 10 for both equations.

Answer 25

so it makes 11x + 14y = 2615 and 12x + 18y = 3180

Answer 26

11x+14y=2615
12x+18y=3180

Answer 27

yes. now we just solve that. it's gonna be a lil messy, i guess.

Answer 28

do you need help with solving the equations?

Answer 29

should be 85 racing and 120 mtn bikes

Answer 30

well that was fast. yeah that does work.

Answer 31

good job! any question?

Answer 32

ya but i dont know how that is

Answer 33

how do i eliminate

Answer 34

what do 11 and twelve have in common

Answer 35

132.

Answer 36

but you wouldn't go for the 11 and 12. that's too much.

Answer 37

try 14 and 18.

Answer 38

9 and 7

Answer 39

and dont forget 2. 9/7/2

Answer 40

but you probably used your graphing calculator to solve it. i don't think you'll ever need to solve it only with your hands only. so don't worry too much about it.

Answer 41

thans!!!

Answer 42

thanks* :P

Answer 43

no problem. :)