$8\mathrm{.}9.$ The management of the Albert Hanson Company is trying to determine the best product mix for two new products. Because these products would share the same production facili$-$ ties, the total number of units produced of the two products com$-$ bined cannot exceed two per hour. Because of uncertainty about how well these products will sell, the profit from producing each product provides decreasing marginal returns as the production rate is increased. In particular, with a production rate of Ri units per hour, it is estimated that Product $1$ would provide a profit per hour of $$200$R$,$ S$100$R$.$ If the production rate of product $2$ is R units per hour, its estimated profit per hour would be S$300$R$2$ $$100$R$2.$ a$.$ Formulate a quadratic programming model in alge$-$ braic form for determining the product mix that maximizes the total profit per hour. Formulate this model on a spreadsheet. E$*$ b$.$ c$.$ Use RSPE's Analyze without Solving feature to confirm that the model is QP Convex. d$.$ Solve the model using the appropriate solving method.