(Solved): food producer uses two processing plants, P1 and P2, which operate seven days a week. After p ...

food producer uses two processing plants, $$P_1$$ and $$P_2$$, which operate seven days a week. After processing, beef is araded into high-, medium- and low-quality foodstuffs. High-quality beef is soid to butchers, medium-quality beef is used in supermarket ready meals and the low quality beef is used in dog food. The producer has contracted to provide $$120\mathrm{kg}$$ of high-, $$80\mathrm{kg}$$ of medium-and $$240\mathrm{kg}$$ of low-quality beef each week. It costs $$\$4000$$ per day to run plant $$P_1$$ and $$\$3200$$ per day to run plant $$P_2$$. Each day $$P_1$$ processes $$60\mathrm{kg}$$ of high-quality beef, $$20\mathrm{kg}$$ of medium-quality beef and $$40\mathrm{kg}$$ of low-quality beef. The corresponding quantities for $$P_2$$ are $$20\mathrm{kg},20\mathrm{kg}$$ and $$120\mathrm{kg}$$, respectively. a) What are the constraints to satisfy (apart from having values for days between 0 and 7)? Constraint 1: Constraint 2: Constraint 3: b) What are the vertices of the solution set (i.e, the intersection points)? (Sort your answers from the smallest value for P1 to the largest) $$\begin{array}{l}{P}_1=x,P_2=x\\ P_1=x,P_2=x\\ P_1=x\\ P_1=P_2=x,P_2=x\end{array}$$