I have no clue how to solve this please explain it

[NerdBoy628]

A company produces packs of pencils and pens. The company produces at least 30 packs of pens each day but no more than 40. The company produces at least 90 packs of pencils each day but no more than 110. A total of less than 130 packs of pens and pencils are produced each day. Each pack of pens makes a profit of 2.20, and each pack of pencils makes a profit of 1.25. What is the maximum profit the company can make each day?

 

[khansaheb]

A company produces packs of pencils and pens. The company produces at least 30 packs of pens each day but no more than 40. The company produces at least 90 packs of pencils each day but no more than 110. A total of less than 130 packs of pens and pencils are produced each day. Each pack of pens makes a profit of 2.20, and each pack of pencils makes a profit of 1.25. What is the maximum profit the company can make each day?

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[Steven G]

Let x = the number of pencils you produce.
Let y = the number of pens that you produce.

The company produces at least 30 packs of pens each day but no more than 40. 30<y<40
The company produces at least 90 packs of pencils each day but no more than 110. ????
A total of less than 130 packs of pens and pencils are produced each day. ?????
Each pack of pens makes a profit of 2.20, and each pack of pencils makes a profit of 1.25. What is the profit the company can make each day in terms of x and y? ????
Now the problem really starts as you have to find the maximum profit the company can make each day

 

[The Highlander]

A company produces packs of pencils and pens. The company produces at least 30 packs of pens each day but no more than 40. The company produces at least 90 packs of pencils each day but no more than 110. A total of less than 130 packs of pens and pencils are produced each day. Each pack of pens makes a profit of 2.20, and each pack of pencils makes a profit of 1.25. What is the maximum profit the company can make each day?

The company will maximize its profit when it produces as many packs as it can, ie: 129. (Because less than "130 packs of pens and pencils are produced each day.".)

(You really should include a currency symbol when dealing with money matters; so I will use "$".)

The profit from 1 pack of pens is $2.20, therefore, the profit from 20 packs is 20 × $2.20 = $44.00.

Packs of pens produce $0.95 more than packs of pencils, therefore, the company should produce as many packs of pens as possible to maximize its profit.

However, if it were to produce the 40 packs of pens it can in a day, then that would mean only 89 packs of pencils were produced (129 - 40 = 89) but that is not allowed! (They must produce at least 90 packs of pencils.)

So what is the greatest number of packs of pens that they can produce?

Can you now work out what number of packs of each product (pens & pencils) would be to get the maximum daily profit and how much that profit would be?

Please come back and show us your working and answer (a picture will do).
Hope that helps.