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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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