Question 5: Resource Allocation and Production Planning (20 points)A small business produces two products, P and Q , using two resources: labour hours and machine hours.Each unit of P requires 2 labour hours and 1 machine hour.Each unit of Q requires 1 labour hour and 3 machine hours.The company can allocate a maximum of 300 labour hours and 360 machine hours.a.(3 points) Define variables for the number of units of P and Q produced, and write the system of equations Ax=B representing the resource allocation.b.(11 points) Find A-1 and use it to solve for X .c.(3 points) Interpret the result: how many units of P and Q should be produced to exactly use up the available resources?d.(3 points) Briefly discuss how changes in available labour (e.g., an additional 20 hours) would affect the production quantities.