## bii17 3 years ago The unit price of manufacturing a product is P=200-0.01x where x is the number of units produced. assuming all units are sold. a. what value of production (units) will yield a maximum sales? b. what is the value of maximum sales? c. what is the unit price at maximum sales level? plss. help thank you

1. LolWolf

If we define x as the number of units produced, we the receive that the total production cost is: $xP=200x-0.01x^2$So, we find the maxima of this curve, one way to do this is differentiation, although your teacher may have taught you a few others: $(xP)'=200-0.02x=0\\ x=10000$Which means that, we have minimized the cost per unit at this point. (A) the value of sales is $10000P(x)=10000\cdot(200-10000\cdot0.01)=10^6$Which is our answer to B. And, as the previous, we simply take $P(x)=200-0.01\cdot10000=100$ For C.

2. dumbcow

sales = price * num of units sales = P(x) * x sales = 200x - .01x^2 this is a parabola...to get maximum, find vertex y = -.01x^2 +200x + 0 x_coord of vertex = -b/2a where a,b,c are coefficients x = -200/-.02 = 10,000 plug this in to get y_coord of vertex

3. dumbcow

@LolWolf way is better...assuming you know calculus

4. LolWolf

If you don't, you @dumbcow 's way to find the maxima works equally as well.

5. bii17

its for our calculus .. Thank you guys for your help. i get it.. Thak you @LolWolf @dumbcow