A company produces two varieties of pens: alpha and beta. Each alpha pen needs twice as much labour time as the beta pen. If only beta pens are manufactured, then the company can produce 500 pens per day. The market can take only up to 150 alpha pens and 250 beta pens per day from the company. The profits earned by the company on selling an alpha pen and a beta pen are Rs 8 and Rs 5 respectively. What are the respective numbers of alpha and beta pens that the company needs to produce in order to maximize the profit?

Question

dumbcow · Answer

there are three constraints,
Let A be # of alpha pens, B is # of beta pens
2A + B < 500
A < 150
B < 250

the profit function:
P = 8A +5B

Graph the constraints and find the point which maximizes profit
this point will always be on outside line at a distinct vertex where two constraints meet