8. From time to time a department will reallocate some space among its various departments. One simple approach is to approximate the average profit per square meter per year for a department as a linear function of the space allocated to the department. One then tries to find an allocation which maximizes the total profit. Suppose that we have a modest little store with but two departments: Odds and Ends. The managers of these departments were asked to each give two point estimates of the yearly profit per square meter as a function of the number of square meters allocated. These are shown below: Odds Ends Sq. M. of Space $/(Sq. M* Yr) Sq. M. of Space $/(Sq. M* Yr) min space 9 $12,000 12 $15,000 max space 50 $5,000 45 $4,000 There are a total of 65 square meters of space to be allocated. Further, each department will be allocated neither less than the minimum space shown for it in the above table nor more than the max space. It is assumed that between the min and max allocations the average profit/(square meter * year) is a linear function of space allocated. neter is