Help please!
btw the 'ṗ' below is supposed to be a p with a line over the top.
Find the producer's surplus at a price level of ṗ = 380 for the price-demand equation p = D[x] = 0.005x^2 + 0.8 + 20.
2007-04-25 09:11:00 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
If I understand your question rigth, I believe this is what you are looking for.
D[x] = 0.005x² + 0.8 + 20
D[380] = 0.005(380)² + 0.8 + 20
D[380] = 0.005(380)² + 0.8 + 20
D[380] = 0.005(144,400) + 0.8 + 20
D[380] = 3∙61 + 0.8 + 20
D[380] = 24∙41
2007-04-25 09:23:12 · answer #1 · answered by Sparks 6 · 0⤊ 0⤋
á¹ = (1/x)â«(0.005x^2) + 0.8x + 20)dx
á¹ = (1/x)[(0.005/3)x^3 + 0.4x^2 + 20x]
á¹ = (0.005/3)x^2 + 0.4x + 20 = 380
0.005x^2 + 0.12x + 60 = 1140
x^2 + 24x = 228000 - 12000
x^2 + 24x + 144 = 216000 + 144
(x + 12)^2 = 216144
x + 12 = â216144 = 464.91
x = 452.91
rounding up,
x = 453
p(453) = 0.005(453)^2 + 0.8*453 + 20
p(453) = $1,408.45
2007-04-25 16:51:57 · answer #2 · answered by Helmut 7 · 0⤊ 0⤋