Question

Please help with this calculus problem!



Leopard golf clubs usually sell for $1300. At this price, the retailer can sell, on average, 20 sets per week. For every $50 reduction in price, sales of the golf clubs increase by two sets per week. Similarly, for every $50 increase in price, sales decrease by two sets per week. Determine the optimum price to maximize revenue.

Answer 1

R = (1300-50x)(20-2x)
Find R', and then set it equal to 0 and solve for x.

Answer 2

Then what do you do after finding x?

Answer 3

Sorry thats, (20+2x) *

Answer 4

Once you have found x, then you can apply it to 1300-50x, giving you the optimum price to sell it at.

Answer 5

so you substitue x into 1300-5x?

Answer 6

x = 18 btw

Answer 7

You should have x = 8 as your answer, then the optimum price will be 1300-5*8 = 1260.

Answer 8

I made the typo in the original equation it should be R = (1300-50x)(20+2x)

Answer 9

oo nvm i used 20-2x :P

Answer 10

i got x as 13 now

Answer 11

I don't think that's correct, I am getting 8 still.

Answer 12

nvm ye now i got 8

Answer 13

yes it is 8

Answer 14

no need for calc , just have
\[-100 x^2+1600 x+26000\]vertex is at \(-\frac{b}{2a}=8\)

Answer 15

yes, i got 8, now what?

Answer 16

The optimal price is the one where it is 1300-50x, so you plug in x.

Answer 17

so 1300-50(8)?

Answer 18

Yup

Answer 19

Thats the final answer??

Answer 20

Yes that will result in the optimal price.

Answer 21

Ok thank you so much