Question

A company that produces ribbon has found that the marginal cost of producing x yards of fancy ribbon is given by Upper C prime left parenthesis x right parenthesisC′(x)equals=negative 0.00001 x squared minus 0.02 x plus 49−0.00001x2−0.02x+49 for x less than or equals 1400x≤1400​, where Upper C prime left parenthesis x right parenthesisC′(x) is in cents. Approximate the total cost of manufacturing 14001400 yards of​ ribbon, using 5 subintervals over left bracket 0 comma 1400 right bracket[0,1400] and the left endpoint of each subinterval.

Answer 1

Explanation:

Given:

`<strong>C_((x))=-0.00001x^(2)-0.02x+49</strong>`

for x≤1400; N = 5

So, Δx =
`(1400-0)/(5) =280\\\\\int\limits^(1400)_0 {C(x)} \, dx`=∑C(a + nΔx).Δx

=C(0)Δx + C(280)Δx + C(560)Δx + C(840)Δx + C(1120)Δx

= Δx[C(0) + C(280) + C(560) + C(840) + C(1120)]

= 280[49 + 42.616 + 34.664 + 25.144 + 14.056]

=280[165.48]

=46334 approx