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DerKrebs [107]
3 years ago
12

Brach and Larue is a home goods store chain, and it is about to introduce a new convection oven that’s expected to sell very wel

l across its stores. These are the projected revenue and cost functions for the ovens:
R(x) = -13.85x2 + 1,660x
C(x) = 55,400 – 279x

What is the maximum profit that can be made from selling the ovens?
Mathematics
1 answer:
zvonat [6]3 years ago
6 0

Answer:

\$12,465

Step-by-step explanation:

The functions for cost and revenue are given below:

Projected \:Revenue,R(x)=  -13.85x^2 + 1660x\\$Projected Cost, C(x)=55400 -279x\\Projected Profit = Revenue-Cost=R(x)-C(x)\\=-13.85x^2 + 1660x-(55400 -279x)\\=-13.85x^2 + 1660x-55400 +279x\\P(x)=-13.85x^2 + 1939x-55400

The profit will be maximized at its <u>line of symmetry,</u>x=-\dfrac{b}{2a}<u />

From P(x), a=-13.85, b=1939

<u>Line of symmetry,</u>

<u />x=-\dfrac{b}{2a}=-\dfrac{1939}{2(-13.85)}=70<u />

<u>The maximum profit that can be made will occur when x=70</u>

<u />P(x)=-13.85x^2 + 1939x-55400\\P(70)=-13.85(70)^2 + 1939(70)-55400\\=\$12,465<u />

The maximum profit that can be made form the sales of the oven is $12,465.

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If 70% is £14 what is the full price
Veseljchak [2.6K]
70℅ = 14
100 = X

70X = 1400

X = 1400/70

X = 20

20 Euros is the full price
6 0
3 years ago
A county's population in 1991 was 147 million. In 1998 it was 153 million. Estimate the population in 2017 using the exponential
aliina [53]
Let t=number of years since 1991.
Then 
P(t)=147 e^(kt)   ... in millions
P(0)=147 e^(0)=147
P(7)=147 e^(7k)=153
e^(7k)=(153/147)
take ln both sides
ln(e^(7k))=ln(153/147)
7k=0.0400 => k=0.005715

Year 2017=>t=2017-1991=26
P(26)=147e^(26*.005715)=170.55
Answer: in 2017, the projected population is 170.55 millions.
6 0
3 years ago
Help me with this questing plsss
docker41 [41]

Answer:

6.25n + 3.50

$34.75

Step-by-step explanation:

Break down the important information given in the problem.

The one-time delivery fee is 3.50. This is only paid one time an never again, making it the <u>constant</u>, a number that does not change.

Each lunch costs 6.25. This amount will increase depending on how many times Mr. Jackson orders lunches, "n" times. This number is the <u>rate</u> because it changes. The rate is attached to the variable.

If you add the amounts together, that is the total cost of ordering lunches.

6.25n + 3.50

(Reember expressions do not have the equal sign).

To find the cost of ordering 5 lunches, use the expression. Substitute "n" for 5 because "n" represents the number of lunches ordered.

6.25n + 3.50

= 6.25(5) + 3.50   Simplify by multiplying 5 and 6.25

= 31.25 + 3.50    Add the two values

= 34.75       Total cost of 5 lunches

Therefore the cost of ordering 5 lunches is $34.75.

8 0
3 years ago
For the percent 82%, (a) write a decimal and (b) write a fraction in lowest terms.
ale4655 [162]

Answer:

.82

41/50

Step-by-step explanation:

82%

Move the decimal 2 places to the left to change to decimal form

.82

Percent means out of 100

82/100

Divide by 2

41/50

3 0
3 years ago
Read 2 more answers
After 8 points are added to each score in a sample, the mean is found to be M= 40. What was the value for the original mean
MArishka [77]

Answer:

The value for the original mean = 32

Step-by-step explanation:

Here, we want to calculate the original value of the mean.

Let the number of samples be n

Mathematically;

mean = Total value/n

Now, we added 8 to each of values; total value added = 8 * n = 8n

Now, for the new mean of 40; we have

(Total value + 8n)/n = 40

Total value + 8n = 40n

Total value = 40n -8n

Total value = 32n

kindly recall from the beginning of the solution;

mean = Total value/n

mean = 32n/n

mean = 32

So the original value of the mean is 32

6 0
3 years ago
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