Q3 Use a matrix method to find the equilibrium prices and quantities where the supply and demand functions for Good 1, Good 2 and Good 3 are as Qd1 = 50 − 2P1 + 5P2 − 3P3, Qs1 = 8P1 − 5 Qd2 = 22 + 7P1 − 2P2 + 5P3, Qs2 = 12P2 − 5 Qd3 = 17 + P1 + 5P2 − 3P3, Qs3 = 4P3 − 1 Q4 (i) A business manager determines that t months after production begins on a new product, the number of units produced will be P thousand, where P(t) = 6?2 + 5? (? + 1)2. What happens to production in the long run? (ii) A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a distance x meters from the rupture. Turbulence makes it difficult to directly measure the thickness of the slick at the source (where x = 0), but for x > 0,it is found that y = 0.5(x2 + 3x) x3 + x2 + 4x. Assuming the oil slick is continuously distributed, how thick would you expect it to be at the source?
Q3
Use a matrix method to find the equilibrium prices and quantities where the supply and demand functions for Good 1, Good 2 and Good 3 are as
Qd1 = 50 − 2P1 + 5P2 − 3P3, Qs1 = 8P1 − 5
Qd2 = 22 + 7P1 − 2P2 + 5P3, Qs2 = 12P2 − 5
Qd3 = 17 + P1 + 5P2 − 3P3, Qs3 = 4P3 − 1
Q4
(i) A business manager determines that t months after production begins on a new product,
the number of units produced will be P thousand, where P(t) = 6?2 + 5? (? + 1)2
.
What happens to production in the long run?
(ii) A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a distance x meters from the rupture. Turbulence makes it difficult to directly measure the thickness of the slick at the source (where x = 0), but for x > 0,it is found that y = 0.5(x2 + 3x) x3 + x2 + 4x
. Assuming the oil slick is continuously distributed, how thick would you expect it to be at the source?
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