8. The Pat-A-Cake Shop makes chocolate cake in 3 sizes - small, medium, and large. The shop has the following amounts of the three main ingredients on hand -400 ounces of cake flour, 550 ounces of caster sugar, and 150 ounces of cocoa powder. The table below provides details on the amount of each ingredient required for each cake size as well as the profit contributions. Cake Cake flour small 8 (ounce) medium large Available 16 21 400 Cane sugar (ounce) 18 22 25 550 Cocoa powder (ounce) 3 5 11 150 Profit Unit $18 $25 $32 Develop and solve a linear programming model to maximize profit. What is the optimal solution for the number of small cakes made? (round the answer to three decimal places)