Business and Economic Applications Show all work including a

Business and Economic Applications. Show all work including any useful sketches, the function of to be integrated, and the calculation of the definite integral. Clearly label all answers and intermediate values with the appropriate units. The marginal cost of a company is given by C(q) = 3 - 0.02q + 0.006q^2 where q is the number of units produced. What is the total cost to raise production from 90 units to 180 units? Probability Density Functions. Show all work including any useful sketches of the function to be integrated, and the calculation of the definite integral. Clearly label all answers and intermediate values with the appropriate units. The Statistics Aptitude Test (SAT) is normed or standardized to have a mean of 100 points and a standard deviation of 20 points. Find the probability that a randomly selected individual will score between 70 points and 115 points.

Solution

16)

C(q) = 3-0.02q+0.006q^2

here q =the number of units produced

total cost to raise proudction from 90 units to 180units

total cost = integral (90 to 180 ) C(q) dq

= integral (90 to 180) [  3-0.02q+0.006q^2 ] dq

= (q=90 to q=180) [ 3q -0.02 q^2 /2 +0.006q^3 /3 ]

= [ 3q -0.01q^2 +0.002q^3] from(90 to 180 )

= [ 3x180 -0.01(180)^2 +0.002(180)^3] - [ 3x90 -0.01(90)^2 +0.002(90)^3 ]

= [ 540 -324 +11664] - [ 270- 81 +1458]

= [216 +11664] - [189+1458]

= [11880 ] - [1647]

= 10233

total cost =10233