Parker Pens Inc (PPI) produces five different models of pens: Alpha, Bravo, Charlie, Delta, and Echo. Each pen requires up to four ingredients steel, gold, silver, and rubber. Weights of ingredients needed per pen for each model of pen is specified below along with the maximum monthly demand and profit per pen for each model of pen. PPI must purchase all of the needed ingredients from a single supplier, and the supplier is able to supply only 12,000 kilograms of Steel, 120 kilogram of gold, 240 kilogram of silver, and 6000 kilograms of rubber per year (equally distributed across 12 months). To keep its network of retailers committed to selling different models of its pens, PPI must produce at least 10% of the expected demand of each model of pen (except for Delta) every month. Decide how many pens of each type should PPI make per month to maximize its monthly profit given the stated constraints. (50 points) Note: 1 kilogram = 1,000 grams Pen Model Profit per pen Monthly Demand Steel needed per pen Gold needed per pen Silver needed per pen Rubber needed per pen Alpha $79 1,000 10 grams 15 grams 6 grams 0 gram Bravo $69 1,500 11 grams 6 grams 16 grams 0 gram Charlie $29 2,000 12 grams 1 gram 1 gram 0 gram Delta $5 5,000 13 grams 0 gram 2 grams 5 grams Echo $1 10,000 14 grams 0 gram 0 gram 10 grams

b) Find the correct optimal solution through the graphing method. (15 points) i. 5 points for correct x and y intercepts for each constraint (along with relevant calculations). ii. 5 points for correct coordinates of points where constraint lines intersect (along with relevant calculations). iii. 3 points for showing correct feasible region on the graph. iv. 2 points for correct optimal solution & objective value (along with relevant calculations).