I would appreciate it if someone helped me with this problem?

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

Well I'd say time is a constraint. you only have so many hours per week.

You need to set up a quadratic equation to describe the process.

varibles will be profit P, time x3 in hours (TA, TM, TI) (for assemble, manufacture and inspection), number of board NB, number of electronic NE

P = NB*$10 + NE*$15

NB=TA*1/2+TM*1/2+ TI*1/4

NE=TA*/21+TM*1+TI*1/2

put NB and NE into the P equation. And then do triple intergral for TM = 0 to 40, TA = 0 to 32 and TI = 0 to 18.

something like that. If you don't know about triple intergrals, I'm sorry I don't know the answer