Verify that the vector X is a solution of the given homogeneous system. dx / dt = 3x − 3y
dy /dt = 3x − 7y;
X = (1 /3) e^−6t

Writing the system in the form X' = AX for some coefficient matrix A, one obtains the following:

X'= [ ] X

Tom is the deli manager at a grocery store. he needs to schedule employee to staff the deli department for no more that 260 person-hours per week. tom has one part-time employee who works 20 person-hours per week. each full-time employee works 40 person-hours per week. write and inequality to determine n, the number of full-time employees tom may schedule, so that his employees work on more than 260 person-hours per week. graph the solution set to this inequality.