Question

The marginal cost of drilling an oil well depends on the depth at which you are drilling; drilling becomes more expensive, per meter, as you dig deeper into the earth. The fixed costs are 1,000,000 riyals (the riyal is the unit of currency of Saudi Arabia), and, if x is the depth in meters, the marginal costs are C' (x) = 4000 + 10x (Riyals/meter).Find the total cost of drilling a 500-meter well.

Answer 1

Answer:

4,250,000 riyals

Step-by-step explanation:

The total cost of drilling a 500-meter well is the sum of fixed costs (1,000,000 riyals) and variable costs.

By integrating the marginal cost function we get the variable costs function. Evaluating the variable costs function from 0 to 500 meters, gives us the total variable cost.

$C(x) =\int\limits^{500}_0 {C(x')} \, dx =\int\limits^{500}_0 {(4000 + 10x)} \, dx \\C(x)=4000x +5x^2 +c|^{500}_0\\C(500) - C(0) = (4000*500 +5*500^2 +c) - (4000*0 +5*0^2 +c)\\C(500) - C(0) = 3,250,000$

Total cost of drilling is:

$TC = 3,250,000 + 1,000,000\\TC = 4,250,000\ riyals$