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scZoUnD [109]
3 years ago
12

The demand function for a type of portable radio is given by the model d=85−6x2, where d is measured in dollars and x is measure

d in millions of units. The production cost is $25.00 per radio. Given that profit = revenue - costs answer the following parts. (Hint: Revenue is demand times number sold. Costs are productions costs per number sold.)
Part A: Write an equation giving profit as a function of x million radios sold. Part B: The company currently produces 3 million radios and makes a profit of $18,000,000, but would like to scale back production. What lesser number of radios could the company produce to yield the same profit?
Part C: Give a graph for the profit and label the parts of the graph.

Mathematics
1 answer:
Lostsunrise [7]3 years ago
3 0

Answer:

Part A : The required Profit equation : \text{Profit}= 60x-6x^3

Part B : 0.303 million radios the profit became 18 million.

Part C : The graph is attached below.

Step-by-step explanation:

Given : The demand function for a type of portable radio is given by the model d=85-6x^2, where d is measured in dollars and x is measured in millions of units. The production cost is $25.00 per radio.  

Note: Given that profit = revenue - costs

Revenue is demand times number sold.

Costs are productions costs per number sold.

To find :

Part A: Write an equation giving profit as a function of x million radios sold.

Solution : Let x be the number of radios.

Revenue is demand times number sold

\text{Revenue}= x\times (85-6x^2)

\text{Revenue}= 85x-6x^3

Let the cost of x number of radios is 25x.            

Profit = Revenue - Costs

\text{Profit}= 85x-6x^3-25x

P(x)= 60x-6x^3

The required Profit equation : P(x)= 60x-6x^3

 

Part B : The company currently produces 3 million radios and makes a profit of $18,000,000, but would like to scale back production. What lesser number of radios could the company produce to yield the same profit?

Solution :  It is shown graphically which is attached in part c

When we scale back production we get that,

When we sold 0.303 million radios the profit became 18 million.

Part C : Give a graph for the profit and label the parts of the graph.

The graph is attached below which shows the profitable radios points.

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Nataly_w [17]

Answer:

i) -28 ft/s

ii) -21.6 ft/s

iii) -20.8 ft/s

iv) -20.16 ft/s

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Step-by-step explanation:

if v represents vertical velocity then if the height y is

y = 44*t − 16*t²

and the instant velocity v is the derivative with respect to the time

v= dy/dt = 44*(1) - 16*(2*t) = 44- 32*t

while the average velocity is va= (y-y₀)/(t-t₀)

where t₀ = 2 and y₀=y(t₀) =  44*2 − 16*2² = 24

then

va= (y-y₀)/(t-t₀) = (44*t − 16*t² -  24)/(t-2)

for

i) t= 0.5s + 2 s= 2.5 s

va = (44* 2.5  − 16* 2.5 ² -  24)/( 2.5 -2) = -28 ft/s

ii) t= 0.1s + 2 s= 2.1 s

va = (44* 2.1  − 16* 2.1 ² -  24)/( 2.1 -2) = -21.6 ft/s

iii) t= 0.05 s + 2 s= 2.05 s

va = (44* 2.05  − 16* 2.05 ² -  24)/( 2.05 -2) = -20.8 ft/s

iv) t= 0.01s + 2 s= 2.01 s

va = (44* 2.01  − 16* 2.01 ² -  24)/( 2.01 -2) = -20.16 ft/s

b) the instantaneous velocity when t=2

v (t=2) =  44- 32*(2) = -20 ft/s

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On a certain marathon course a runner reaches a big hill that is at least 10 miles into the race. If a total marathon is 26.2 mi
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8 0
3 years ago
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8 0
3 years ago
Would I use subtraction for this problem ?
garik1379 [7]

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4 0
2 years ago
NEED HELP ASAP ILL MAKE YOU BRAINLIEST
Hunter-Best [27]

y = 12000x + 35000


When Mr. Nicolas began recording, it means, at 0 hour, how many tortillas was produced?


Subs x by 0.


y = 12000.0 + 35000

y = 0 + 35000

y = 35000


When Mr. Nicolas began recording the data, 35,000 tortillas had already been produced


The total number of tortillas produced 2 hours after the he began, it means, when x = 2


y = 12000 . 2 + 35000

y = 24000 + 35000

y = 59000


The total number of tortillas produced 2 hours after he began recording the data was 59,000


The total number of tortillas produced _ hours after he began recording the data was 85,000


Now we have y but not x.


y = 12,000x + 35,000

85,000 = 12,000x + 35,000

85,000 - 35,000 = 12,000x

50,000 = 12,000x

x = 50/12

x = 25/6

x = 4,1666...

Rounding

x = 4,167

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3 years ago
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