An oil refinery produces oil at a variable rate given by the following equation, where t is measured in days and q is measure in barrels. upper q prime left parenthesis t right start 3 by 2 matrix 1st row 1st column 600 2nd column if 0 less than or equals t less than 30 2nd row 1st column 2500 minus 50 t 2nd column if 30 less than or equals t less than 40 3rd row 1st column 400 2nd column if t greater than or equals 40 endmatrix a. how many barrels are produced in the first 35 days? b. how many barrels are produced in the first 50 days? c. without using calculus, determine the number of barrels produced over the interval [70,90].