Luke is having a rectangular swimming pool built in his back yard. he wants it to be 30 feet longer than it is wide. he also has to decide how deep he wants the pool to be. he wants the width of the pool to be at least 15 feet greater than the depth. the cost of the pool will be based on the depth and area of the pool. the cost of the pool will be $10 per square foot of perimeter plus $30 per foot of depth. luke can afford to spend no more than $15,000 on the construction of the pool. create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.