The profit function for Wannamaker Trophies is P(x) = -0.3x2 + fx - m, where f represents the design fee for a customer’s awards and m represents the monthly office rent. Also, P represents the monthly profit in dollars of the small business where x is the number of awards designed in that month.
a) If $60 is charged for a design fee, and the monthly studio rent is $1,500; write an equation for the profit, P, in terms of x.
Typing hint: Type x-squared as x^2
Answer: P(x) = -0.3x^2 + fx – m
Given: f = 60 and m = 1500.
Simply plug in these values into the equation above.
b) How much is the profit when 50 award designs are sold in a month?
Answer: If x= the # of awards designed per month, and there are 50 awards designed in 1 month, then for this particular set of circumstances, x=50.
Show your work here: you just pug x=50 into the equation from part a) and solve for P(x).
c)
Answer: To find how many awards need to be designed for maximum profit (x) then all you need to do is use the 2ax = -b formula to solve for x.
Show your work here: the extreme point expression, 2ax=-b
Is actually the formula for finding the x-coordinate of the vertex. If you
graph -0.3x^2 + 60x - 1500, you will find that it is a parabola that opens
down (umbrella shaped) so then you know that the vertex is going to be a
maximum. If it is a parabola that opens up (u shaped) then you know that it
is a minimum. (Parabolas that open downward have a negative a-value and
parabolas that open up have a positive a-value.
d) What is the maximum profit?
Answer:
Show your work here:
