Question

The supply function for manufacturing a certain item is p(x)=x2+46x−66. The demand function is p(x)=56x+30. If x represents the number of items (in hundreds), what is the optimum number of items to be manufactured?

Answer 1

welcome to QC ~

optimum occurs at supply = demand

so set x^2 + 46x - 66 = 56x + 30 and solve for x

Answer 2

ok brb

Answer 3

600?

Answer 4

Hm, not quite

can you try combining like terms?

Answer 5

x^2 + 46x - 66 = 56x + 30

for example, you can subtract 56x from both sides, what do you get after that?

Answer 6

i did i put all the xs to the right so i got 10x some how

Answer 7

10x

Answer 8

hm, let's try putting all the x terms on the left instead

Answer 9

can you try subtracting 56x from both sides?

Answer 10

oh nvm i subtracted 46

Answer 11

well i still got 10x

Answer 12

ok

Answer 13

x^2 + 46x - 66 - 56x = ?

Answer 14

yes i just combined like terms now it is x^2+10x-66

Answer 15

almost, since it's 46x - 56x it's -10x not positive 10x

so right now we have

x^2 - 10x - 66 = 30

now try subtracting 30 from both sides

Answer 16

ok

Answer 17

i got x^2+10x-36

Answer 18

hm, not quite, remember the rules for subtracting signs

-66 - 30 = -96

Answer 19

ohh ok

Answer 20

now we have

x^2 - 10x - 96 = 0

can you try factoring this? as a hint try to find two numbers that multiply to get -96 and add up to get -10

Answer 21

ok ill try

Answer 22

6 and -16 ?

Answer 23

awesome

so our eqn becomes

(x+6)(x-16) = 0

splitting this into two parts gives us

x + 6 = 0
x - 16 = 0

so what are the two values of x?

Answer 24

x=6 x=-16

Answer 25

hm, not quite

x + 6 = 0

subtracting 6 from both sides gives us

x = -6, not positive 6

same thing with x - 16 = 0, adding 16 to both sides gives us x = 16

Answer 26

ohh

Answer 27

that being said, since x represents the # of items in the 100's, that means x must be positive

so we take the positive solution 16 and multiply by 100 to get the sol'n 1600

Answer 28

oh wow that seems pretty easy now that i know what to do thanks alot have a good day