$(Please$ slove using excel$)$ Health & Comfort, Incorporated $($H&C$)$ specializes in the produc$-$ tion of hypoallergenic pillow and mattress covers for asthma and allergy sufferers. The covers are made out of a unique protective fabric. The manufacturing process consists mainly of two operations: cutting and sewing, which are performed by two separate departments. Table $8\mathrm{.}14$ shows the resource utilization and weekly re$-$ source availability for this problem. H&C is one of the largest producers of hypoallergenic bedding, and it controls a large share of the market. As a consequence, the production level of each product at H&C influences the market price of the product, which in turn influences their unit earnings contributions. Econometric research indicates that this dependence can be represented as: $E_P=506-0\mathrm{.}75$P for pillow covers and $E_M=653\mathrm{.}5-M$ for mattress covers $($here $P$ and $M$ are the production levels of pillow and mattress covers at H&C$,$ and $E_P$and $E_M$are the corresponding unit contributions to earnings in dollars per unit$).$ H&C is seeking to maximize its earnings by selecting appropriate production levels of its products. $(A)$ Formulate a nonlinear optimization model of production for H&C in terms of the variables P$,$M$,E_{P,}$ and $E_M($Note: Your model should have linear constraints and a nonlinear objective function.$)($b$)$Solve the model on the computer. What are the optimal production levels? $\backslash$table$[[,$Pillow Cover,Mattress Cover,Availability per Week$],[$Fabric $($square feet$),8\mathrm{.}75,60\mathrm{.}5,40,000],[$Cutting $($hours$),0\mathrm{.}1,0\mathrm{.}2,150],[$Sewing $($hours$),0\mathrm{.}4,0\mathrm{.}3,500]]$