Someone help ME PLEASE!!!?

Question

a company is making two games. Board and electionic. A board game require 1/2 hour to make, 1/2 hour to assemble, 1/4 hour to inspect and package. (1hr15m). An electronic game requires 1 hour to make, 1/2 hour to assemble and 1/2 hour to inspect/package. (2hours). In a given week, there are 40 hours for manufacturing, 32 hours for assembly and 18 hours for inspection and packaging. Supposed the profit on each board game is $10 and profit for each electronic game is $15. How many of each type should be made to maximiz profit?

Define variables...all I have is:

a= board b= electronic m=manufacturing p=inspection

Write and define constraints...I know I need a in and out table.but don't know what to put in it...I don't have constraints.

Graph feasible region. What is the profit statement?

Use a profit line to find the minimim point on your graph. Use algebra to solve for exact point. Show algebra....wtf am I suppose to do?

How much money should the co. expect to make?

Ok, I'm really lost here idk what to do. If you would please help me understand how to work it out step by step, I would appreciate it..

Answer 1

(Beginning constraints)

X is number of board games

Y is number of electronic games

.5X+Y=40 hours of manufacturing

.5X+.5Y=32 hours of assembling

.25X+.5Y=18 hours of inspection

10X+15Y=Profit

(End of constraints)

So it is constrained between 64 board games (32/.5)

and 36 electronic games (18/.5)

I got these numbers from maximizing number of board games and maximizing number of electronic games.

What you need to do is calculate the profit from having 0 to 36 electronic games and 0 to 64 board games. So like try to figure out what makes the most amount of money by plugging in the values without exceding the constraints (ie. 30 board games, 18 electronic games)

Answer 2

"Al " has the correct idea but you need X=a  Ã¢Â‰Â¥ 0 , Y= b ≥ 0 and then the others are m ≤ 40, p ≤ 18 , a ≤ 32...this gives a fixed region in the 1st quadrant for you to do a Simplex method to determine the point for maximum profit...you do know that if the region is convex then the point is one of the intersection points on the boundary