York Lane Electronics (YLE) sells three popular ball bearings for automobiles: Model S, Model R, and Model T. A unit cost to make Model S is $0.5 (per unit), a unit cost to make Model R is $0.8 (per unit). and a unit cost to make Model T is $1.2 (per unit). The demand for these three ball bearings in Canada is sensitive to price. As the price goes up, the quantity demanded goes down. Historical data indicate that the monthly demands are given by S = 100 - 5P, R = 336 8P2, and T = 560 - 10P3, where S = demand of Model S, R= demand for Model R, T = demand for Model T, P = unit price of Model S, P = unit price of Model R, and P3 = unit price of Model T The Assembly department during COVID-19 period has the limitation of 350 available hours; each Model S ball bearing takes 2 hours; each Model R ball bearing takes 4 hours; each Model T ball bearing takes 7 hours. To reach monthly sales performance, the three ball-bearing models' total demand must be at least 80 units. To remain competitive, YLE must limit the price of Model S and R ball bearings (per unit) to no more than $15 and $40, respectively. Also, considering inventory and other warehousing factors, the demand for maximum Model S, R, and T ball bearings should be 40, 45, and 30 units, respectively. YLE has been interested in finding the optimal demand quantities to maximize total monthly profit. Formulate an unconstrained nonlinear problem and a constrained nonlinear problem in complete formats. Use decision variables S, R, and T only when necessary