(Solved): 1 Glassco manufactures glasses: wine, beer, champagne, and whiskey. Each type of glass requires ti ...

1 Glassco manufactures glasses: wine, beer, champagne, and whiskey. Each type of glass requires time in the molding shop, time in the packaging shop, and a certain amount of glass. The resources required to make each type of glass are given in Table 32. Currently, 600 minutes of molding time, 400 minutes of packaging time, and \( 500 \mathrm{oz} \) of glass are available. Assuming that Glassco wants to maximize revenue, the following LP should be solved: \( \max z=6 x_{1}+10 x_{2}+9 x_{3}+20 x_{4} \) s.t. \( 4 x_{1}+9 x_{2}+7 x_{3}+10 x_{4} \leq 600 \quad \) (Molding \( x_{1}+x_{2}+3 x_{3}+40 x_{4} \leq 400 \quad \) (Packaging constraint) \( 3 x_{1}+4 x_{2}+2 x_{3}+x_{4} \leq 500 \quad \) (Glass constraint) \( x_{1}, x_{2}, x_{3}, x_{4} \geq 0 \) It can be shown that the optimal solution to this \( \mathrm{LP} \) is \( z=\frac{2800}{3} \), \( x_{1}=\frac{400}{3}, x_{4}=\frac{20}{3}, x_{2}=0, x_{3}=0, s_{1}=0, s_{2}=0, s_{3}=\frac{280}{3} \).