Linear Programming

[KEYWEST17]

A manufacturer of downhill and cross-country skis reports that manufacturing time is 1 hours and 4 hours, respectively, per ski and that finishing time is 5 hours for each downhill and 2 hours for each cross-crountry ski. There are only 24 hours per week available for the manufacturing process and 30 hours for the finishing process. The average profit is $50 for downhill ski and $87 for cross-country ski. The manufacturer wants to know how many of each type of ski should be made to maximize the weekly profit.

Corner points of the feasible region:
If there is more than one corner point, type the points separated by a comma (i.e. (1,2),(3,4)).

Maximum profit is: $
when downhill skis______
and________ cross country skis are produced.


So far I set up equations :

x>0
y>0
4x+5y<30
4x+2y<24

Solved for the equations but my end result is incorrect.

 

[tkhunny]

You simply MUST develop useful defintions to START. Don't just schlep through and hope you will remember.

D = # of Downhill Skis
C = # of Cross Country Skis

"downhill and cross-country skis reports that manufacturing time is 1 hours and 4 hours"

We're thinking about 1*D and 4*C.

"finishing time is 5 hours for each downhill and 2 hours for each cross-crountry ski"

We're thinking about 5*D and 2*C

"There are only 24 hours per week available for the manufacturing process"

D + 4C <= 24

"30 hours for the finishing process"

5D + 2C <= 30

"The average profit is $50 for downhill ski and $87 for cross-country ski"

50D + 87C = Total Profit

Just one piece at a time.

Developing the langauge of the defintions freed us not to be confused throughout the rest of the process. Don't skip clear and concise definitions - ever!