The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = 30 + 0.006p3 and that its demand function is D(p) = 150 - 0.12p2, where p is the price. Determine the price for which the supply equals the demand. (5 points)

$22.86
$22.36
$21.36
$21.86

Question

The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = 30 + 0.006p3 and that its demand function is D(p) = 150 - 0.12p2, where p is the price. Determine the price for which the supply equals the demand. (5 points)
 	
	$22.86
	$22.36
	$21.36
	$21.86

campbell_st · Answer

so for supply to equal demand you should have 

S(p) = D(p) 

which means 

$$30 + 0.006p^3 = 150 - 0.12p^2$$

there are 2 ways to do this problem now. 

1. solve for p...which may be difficult given you will have a cubic equation. 

2. Substitute each value form the answer options to find the correct one. 


3. Graph both equations and find the 1st quadrant point of intersection. 


I'd take the substitution option. 

Hope it helps

anonymous · Answer

thank you very much!!