![ayoismeisalex](/avatars/42196.jpg)
ayoismeisalex
13.07.2021 •
Mathematics
6.7.37
Question Help
Ay
60
a
A teenager starts a company selling personalized coffee mugs. The profit
function, in dollars, for producing and selling x mugs is
f(x) = -0.4x?
+ 12x-50, whose graph is shown.
40-
20-
0
TO
-20-
20
a. What are the start-up costs for the teenager's company?
b. How many mugs must the teenager sell before she breaks even?
c. How many mugs will give the maximum profit?
d. What will the profit be if she sells 10 mugs?
30
-407
-60-
Solved
Show answers
More tips
- L Leisure and Entertainment How to Find a Phone Number by Address: The Ultimate Guide...
- P Philosophy How to Properly Create a Vision Board?...
- C Computers and Internet What is Web 2.0 and How Does it Work?...
- S Style and Beauty Is Photoepilation the Solution to Unwanted Hair Forever?...
- O Other What is a Disk Emulsifier and How Does it Work?...
- F Family and Home What does a newborn need?...
- F Family and Home Choosing the Right Car Seat for Your Child: Tips and Recommendations...
- F Food and Cooking How to Get Reconfirmation of Registration?...
- C Computers and Internet How to Get Rid of Spam in ICQ?...
- A Art and Culture Who Said The Less We Love a Woman, the More She Likes Us ?...
Answers on questions: Mathematics
- M Mathematics PLEASE ANYONE HELP I NEED IT DONE BY 11:59 this is the second part to the first part six question all together someone please help...
- M Mathematics Write function PLEASE HELP URGENT WILL GIVE BRAINLIEST...
- M Mathematics Please help with this, i’m not sure what the answer is at all...
- M Mathematics Jesse needs 10 1/4 feet of chain to complete an outdoor project. He has two small pieces each measuring 2 1/8 feet and a third piece measuring 3 3/4 feet. How many...
- M Mathematics the origin is a corner of a square and two of its sides are y + 2 x =0and y + 2 x = 3 find the equation of the other two sides...
- M Mathematics Please answer this question ...
- M Mathematics Help please i need this in less that 3 minutes. i just need the formula or what to do...
- M Mathematics Read the following statement: If m_X = m_Y and m_Y = m_z, then m_X = m_Z. This statement demonstrates: the substitution property. the reflexive property. the symmetric...
- M Mathematics Pls help if you only know the answer! Thanks! :)...
- M Mathematics PLEASE HELP WILL GIVE BRAINLIEST...
Ответ:
a. The start-up cost for the teenagers company is $50
b. The number of mugs the teenager must sell to break even are 5 mugs or 25 mugs
c. The number of mugs that will give maximum profit is 15 mugs
d. The profit if she sells 10 mugs is $30
Step-by-step explanation:
The given profit function for selling x number of mugs is presented as follows;
f(x) = -0.4·x² + 12·x - 50
a. The start-up cost in dollars is given by the value of the profit function at the start, where, x = 0, as follows;
Start-up cost = f(0) = -0.4×0² + 12×0 - 50 = -50
The negative sign represents amount put in the business
The start-up cost = (The initial) $50 put into the business.
b. The break even point is the point where, the revenue and costs are equal
At break even point; Revenue = Cost
∴ Profit, at break even point, f(x) = Revenue - Cost = 0
From the profit function, we get;
At the break even point, f(x) = 0 = -0.4·x² + 12·x - 50
Dividing by -0.4 gives;
0/(-0.4) = 0 = (-0.4·x² + 12·x - 50)/(-0.4) = x² - 30 + 125
0 = x² - 30 + 125
∴ (x - 25)·(x - 5) = 0
The number of mugs the teenager must sell before she breaks even, x = 5 mugs or x = 25 mugs.
c. From the general form of a quadratic equation, which is; y = a··x² + b·x + c, the formula for the x-values at the maximum point is; x = -b/(2·a)
Comparing the profit function to the general form of the quadratic equation we have at the maximum point;
x = -12/(2×(-0.4)) = 15
Therefore, the number of mugs that will give maximum profit, x = 15 mugs.
d. The profit from selling 10 mugs, f(10) is given as follows;
f(10) = -0.4 × 10² + 12 × 10 - 50 = 30
The profit from selling 10 mugs, f(10) = $30
Ответ:
<(5/2)>
Note: 5/2 is determined by multiplying (1/2)(5).