5) The profitfunction for Wannamaker Trophies is P(x) = -0.3x 2 + fx -m, where f
ID: 3096116 • Letter: 5
Question
5) The profitfunction for Wannamaker Trophies is P(x) = -0.3x2 + fx -m, where f represents the design fee for a customer’sawards and m represents the monthly office rent. Also, Prepresents the monthly profit in dollars of the small businesswhere x is the number of awards designed in that month.
a) If $60 ischarged 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+60x-1500
b) How much isthe profit when 50 award designs are sold in a month?
Answer: P(50)=0.3(50)^2+60(50)-1500
Show your work here:
F-design fee $60; m-monthly rent 1,500, P-monthly profit; x=#0faward
P(x) = 0.3x^2+60x-1500
P(x) = 0.3(2500)+3000-1500
P(X) = 50+1500
P(X) = 2,250
c) How manyaward designs must be sold in order to maximize the profit? Show your work algebraically. Trial anderror is not an appropriate method of solution –
use methods taught in class.
Answer:
Show your work here:
d) What is themaximum profit?
Answer:
Show your work here:
Explanation / Answer
First use the formula .... X = b/2a where b = 60 and a = 0.3 (got these from the originalequation) so.................................. X = 60/(2 x .03) X= 100....this is how many must be sold Plug that number into the original equation to getmaximum profit. 0.3(100)2 + 60(100) - 1500 = 3,000 + 6000 -1500 = 7500 is the maximum profitRelated Questions
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