Find the value of x that will return a profit. Cost equation; C=12.30x + 98,000 and the revenue generated by?

Question

the sales is R= 17.98x. A profit is made when the revenue is greater than the cost for x items...
How do I solve this problem???

Answer 1

Cost, C=12.30x + 98000
Revenue, R = 17.98x
A profit when
R > C
17.98x > 12.30x + 98000
5.68x > 98000
x > 17253.521

Answer 2

The equations must be referring to marginal cost, and marginal revenue, which are defined as the slope of the total revenue and total cost curves.
Anti - differentiate both curves to get
a) Total cost

integral of 12.30x + 98,000 = 6.15x^2 + 98,000x
b) total revenue
integral of 17.98x = 8.99x^2.

Then subtract the total revenue by the total cost curve to get total profit.

= (8.99x^2) - (6,15x^2 + 98,000x)
= 2.84x^2 - 98,000x

Graph this function on your calculator, and give the domain for which x yields a positive value.
Or solve explicitly.
2.84x^2 - 98,000x > 0
x(2.84x - 98,000)>0
so 2.84x > 98,000
x> 34507

Answer 3

the cost =revenue equation, then profit begins where the two lines intersect, solving

so set the 2 equal

17.98x=12.30x +98,000

Then5.68x=98,000

And x=17,253.52

Rounded 17,254 I assume it would be $

Answer 4

If c=r, then 17.98x = 12.30x +98000

17.98x - 12.30x = 98000
5.68x = 98000

x = 17253.5211
Therefore for making a profit x should be greater than 17253.5211

Answer 5

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Answer 6

solve 12.30x + 98000 = 17.98x
x=98000/(17.98-12.30)=...

all x's above the solution will have positive profit, so you answer is x>...

Answer 7

17.98x>12.30x+98,000
5.68x>98,000
x>17.254