Maximize profits: how many pens of each type should be made?

[dcc3038026]

Can anybody help with this???

A company manufactures two ballpoint pens, silver and gold. The silver requires 2 min in a grinder and 3 min in a bonder. The gold requires 3 min in a grinder and 9 min in a bonder. The grinder can be run no more than 93 hours per week and the bonder no more than 107 hours per week. The company makes a $6 profit on each silver pen sold and $10 on each gold. How many of each type should be made each week to maximize profits?

 

[Denis]

Re: Maximize profits

What are you looking for? Complete solution?
WHERE are you stuck?

 

[dcc3038026]

This is what I have but it not right.......

Machine Group
Grinder Bonder
Silver 2 mins 3 mins =/< 93hours or 5580 mins
Gold 3 mins 9 mins =/< 107 or 6420 mins


Silver Pens Gold Pens
mins in Grinder 2x + 3y = 5580
mins in Bonder 3x + 9y = 6420
or give the equivalent inequality
x + 3y = 2790
x + 9y = 2140
Number of pens cannot be negative, so
x => 0 and y => 0
Maximize profits z = 6x + 10y

Well...

Maximize z = 10y + 6x
subject to: x + 3y = 2790
x + 9y = 6420
x =/< 0
y =/< 0

Graph a feasible region........
Corner points are: (0 , 237.77) , (0 , 0) , (2140 , 0)

Value of z = 6x + 10y
(0 , 237.77) solved as 6(0) + 10(237.77) = 2377.7
(0 , 0) sovled as 6(0) + 10(0) = 0
(2140, 0) solved as 6(2140) + 10(0) = 12,840 Maximum