An Integral problem. Kindly solve with solutions. Thank you!!!?

Question

The marginal cost of producing x shirts is 30x-10 Dollars. If costs $375 to produce 5 shirts, find the cost of producing 1000 shirts

Answer 1

Cost is the integral of marginal cost:

cost(x) = 15x^2 - 10x + c

Given: $375 for 5 shirts:

cost(5) = 15*5^2 - 10*5 + c
375 = 375 - 50 + c
c = 50

cost(x) = 15x^2 - 10x + 50
cost(1000) = 15*1000^2 - 10*1000 + 50
cost(1000) = $14,990,050

This seems like a crazy amount, but the marginal cost equation says that the cost of the 1,000th shirt is 30*1000-10 = $29,990!

Answer 2

I would think..
Get the indefinite integral of 30x - 10
u shud have 15x^2 - 10x +c
then substitute x for 5 and set the whole equation equal to 375.
U'll see that C = 50
now plug in 1000 for x and there is ur answer.

Since marginal cost function is a derivative of the cost function .. it would make sense to use the integrals to go back to the cost function.

Answer 3

v=u+at v=0 a= -32ft/s^2 t= 1s u=32ft/s v^2=u^2+2as 0=32^2 - 2*32*s s=(32*32)/2*32 =sixteen ft from the right of the living house. height of the living house = optimal height - distance from the right of the living house = 30 - sixteen = 14 ft