SOLUTION: Please show me the way.. A restaurant determined that it's monthly cost function is given by C=3000=16q, where q is the number of dinners sold per month. q=1200-20p, where p is the

Question 83991: Please show me the way.. A restaurant determined that it's monthly cost function is given by C=3000=16q, where q is the number of dinners sold per month. q=1200-20p, where p is the price of the dinner.
a) Solve for p in terms of q and write the revenue and profit as a function of q
b) Find the break even point in terms of q. (the min and max # dinners/mo it can serve without losing $)
c) Write the cost, revenue and profit as functions of p and find breakeven points in terms of p.
d) Determin range of prices for which the restaurant make a profit.
I know this is alot, but I am lost. Any help is appreciated.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A restaurant determined that it's monthly cost function is given by C=3000=16q, where q is the number of dinners sold per month.
q = 1200-20p, where p is the price of the dinner.
:
a) Solve for p in terms of q and write the revenue and profit as a function of q
q = 1200-20p
+20p = 1200 - q
p =
:
Revenue = p * q; substitute for p:
Rev = q()

Rev =
Rev = ; divide both terms by 20
:
Profit = Rev - Cost
:
Profit = (60q - .05q^2) - (3000 + 16q)
:
Profit = 60q - .05q^2 - 3000 - 16q
:
Profit = -.05q^2 + 44q - 3000
:
:
b) Find the break even point in terms of q. (the min and max # dinners/mo it can serve without losing $)
Breakeven point is when profit = 0
:
-.05q^2 + 44q - 3000 = 0
:
Using the quadratic formula, I got:
q ~ 75 meals min and q ~ 805 max, to not lose money
:
Graph this equation:

Profit on the vertical and number of meals on the horizontal
:
:
c) Write the cost, revenue and profit as functions of p and find breakeven points in terms of p.
:
Cost = 3000 + 16q
q = 1200-20p
Replace q with (1200-20p)
Cost = 3000 + 16(1200- 20p)
Cost = 3000 + 19200 - 320p
Cost = 22200 -320p
:
Revenue = p * q
Replace q with (1200-20p)
Rev = p(1200-20p)
Rev = 1200p - 20p^2
:
Profit = Revenue - Cost
Profit = 1200p - 20p^2 - (22200 - 320p)
Profit = 1200p - 20p^2 - 22200 + 320p
Profit = -20p^2 + 1520p - 21000
:
Breakeven is when profit = 0
-20p^2+ 1520p - 21000 = 0
:
:
d) Determine range of prices for which the restaurant make a profit.
:
Solve for p in the above equation: I got p = 18.93 and p = 57.85
Profit between these two values
Graph would look like this:

Profit on the vertical and meal price on the horizonal
:
:
A lot of chance for error here, check my calculations.

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