Calculate the producers' surplus for the supply equation at the indicated unit price p.(Round your answer to the nearest cent.) p = 120 + q; p = 165

ps = 1012.5

Therefore the producers' surplus for the supply equation at the indicated unit price p is 1012.5

Step-by-step explanation:

Given that;

p = 120 + q ; p = 165

Now to find the producer's surplus for supply equation p=f(q) at the indicated unit price; we find p

so from p = 120 + q ; p = 165, if we substitute for q

120 + q = 165

q = 165 - 120 = 45

so

ps = ⁴⁵∫₀ ( 165 - (120+q) dq

ps = ⁴⁵∫₀ ( 45 - q) dq

USING THE EXPRESSION [ xⁿdx = xⁿ⁺¹ / n+1]

ps =  [45q - q²/2]₀⁴⁵

ps = [45(45) - 45²/2] [45(0) - (0)²/2]  

ps =  [2025 - 1012.5] - [0]

ps = 1012.5

Therefore the producers' surplus for the supply equation at the indicated unit price p is 1012.5

Divide both sides by -2.

And/or use the distrubitive property