Linear Programming: maximizing profits on calc. production

J

jshaziza

Junior Member
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Jan 26, 2007
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Almosttexas makes tow types of calculaters. The Deluxe calculator sells for $12, and the Top of the Line calculator sells for $10. It costs Almosttexas $9 to produce a Deluxe and $8 to produce a Top of the Line calculator. In one week, Almosttexas can produce from 200 to 300 Delxe calculators and from 100 to 250 top of the Line calculators, but no more than 500 total calculators. How many of each type should be produced per week to maximize the profits for Almosttexas?

I need to know if the formulas I did for this problem are correct.
P=12x+10y
x=9
y=8
x+y<=500
x<=300
y<=250

Thanks for any help.
 
Re: Linear Programming: maximizing profits on calc. producti

jshaziza said:
Almosttexas makes tow types of calculaters. The Deluxe calculator sells for $12, and the Top of the Line calculator sells for $10. It costs Almosttexas $9 to produce a Deluxe and $8 to produce a Top of the Line calculator. In one week, Almosttexas can produce from 200 to 300 Delxe calculators and from 100 to 250 top of the Line calculators, but no more than 500 total calculators. How many of each type should be produced per week to maximize the profits for Almosttexas?

I need to know if the formulas I did for this problem are correct.
P=12x+10y your profit equation is incorrect ... the right side is revenue, not profit.
x=9 what is this? you are using the variable x to represent the number of deluxe calculators
y=8 ditto
x+y<=500 this is good
x<=300 should be 200 < x < 300
y<=250 should be 100 < y < 250

Thanks for any help.
Click to expand...
 
You seem a little confused.

If x = 9 and y = 8, what is there to maximize?

First, WRITE DOWN clear and precise definitions.

x = # of Deluxe produced
y = # of TOL produced

It doesn't take much, but it will help more than you probably have imagined. Write it down! Trust me on this.

Take another crack at the Maximization formula.

"maximize the profits" You have revenue, not profit.

Try
P = (12-9)x + (10-8)y = 3x + 2y

Get rid of the x = 9 and y = 8 stuff. You may with to add x >= 0 and y >= 0.
 
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