plzzz help me pre calc ans the questions

Question

The Acme Widget Company has found that if widgets are priced at $ 241, then 5000 will be sold. They have also found that for every increase of $ 17, there will be 100 fewer widgets sold. The marginal cost of widgets is $ 84.35. The fixed costs for the Acme Widget Company are $ 36000. If  represents the price of a widget find the following in terms of :

 The number of widgets that will be sold:

The revenue generated by the sale of widgets:

The cost of producing just enough widgets to meet demand:



Find the price that will maximize profits from the sale of widgets: 

The profit from selling widgets:

Answer 1

Demand line: D(x) = mx + b where x is the price...

m = -100/17 and (241,5000)

B = y - mx = 5000 - (-100/17)(241)

= 5000 + 24100/17

= 6417 and 11/17

= 109100/17

THe demand line is:

D(x) = (-100/17) x + (109100/17)

THe cost function is :

C(x) = 84.35x + 36000

The revenue function is R(x) = x *D(x) = x((-100/17) x + (109100/17))

D(x) = C(x)

(-100/17) x + (109100/17) = 84.35x + 36000

109100/17 - 36000 = 84.35x + (100/17)x

multiplies by 17:

109100 - 612000 = 1433.95x + 100x

-502900 = 1533.95x

x = -327.846

The price that maxes the revenue is 54.50...