I have problems to understand and find the equations. AutoTime, a manufacturer of electronic digital timers, has a monthly fixed cost of $46,000 and a production cost of $7 for each timer manufactured. The timers sell for $14 each. (a) What is the cost function C(x)?C(x) = (b) What is the revenue function R(x)?R(x) = (c) What is the profit function P(x)?P(x) = (d) Compute the profit (loss) corresponding to production levels of 3000, 5000, and 13,000 timers, respectively. (Input a negative value to indicate a loss.) 3000 timers $ 5000 timers $ 13,000 timers $

Expert Answers

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Let x be the number of electronic digital timers manufactured or sold in a month.

(a) To set up the cost function, we need to consider the variable cost and the fixed cost.

The variable cost is the production cost, which is $7 for each timer. So the production cost of making x number of timers is 7x.

The fixed cost is the amount $46000 per month.

So the total cost of manufacturing x number of timers in a month is:

`C(x) = 7x + 46000`

(b) The formula for revenue is:

Revenue = Price per unit * quantity sold

The selling price of each timer is $14. So, our revenue function in selling x number of digital timers in a month is:

`R(x) = 14x`

(c) To get the profit in selling x number of digital timers, we have to subtract the total cost from the revenue.

`P(x) = R(x) - C(x)`

Plugging in our revenue function and cost function, this formula becomes:

`P(x) = 14x - (7x + 46000)`

This simplifies to:

`P(x) = 7x - 46000`

This is the profit function in selling x number of digital timers in a month.

(d) The profit/loss when 3000 digital timers is produced and sold is:

`P(3000) = 7(3000) - 46000 = -25000`

Thus, when 3000 timers are produced and sold, there is a loss of $25000.

The profit/loss when 5000 digital timers are produced and sold is:

`P(5000)=7(5000)-46000= -11000`

There is a loss of $11000 when 5000 digital timers are produced and sold.

The profit/loss in producing and selling 13000 digital timers is:

`P(13000)=7(13000)-46000=45000`

Therefore, when 13000 digital timers are produced and sold, there is a profit of $45000.

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