Help! How to calculate maximization?

[mmm3688]

Production plan for softdrinks​

Irene Martin works in a juice firm and has to develop the production plan for the lemon and the orange juice concentrates. The fruits (lemon and orange) that she needs to make the juice are not the bottleneck but Irene is concerned about the other main ingredients that go into making the juice: a water-based solution, sugar, and a vitamin mix. Checking with the ERP system tells her that she has 10900 kg of the water solution, 2970 kg of sugar, and 1990 kg of vitamin mix. The recipe tells her to use 52 kg of water solution to make a metric ton of lemon drink and 75 kg of water solution to make a metric ton of orange drink. For the lemon drink she also needs 24 kg of sugar and 17 kg of vitamin mix. The orange drink needs 11 kg of sugar and 7 kg of vitamin mix.
From the sales department, Ina knows that the lemon soft drink sells at 58 SEK/ton and the orange drink sells at 74 SEK/ton. (SEK = Swedish krona).

1) How much lemon drink should Irene produce to maximize revenue?

2) How much orange drink should Irene produce to maximize revenue?

3)How much revenue can Irene generate with the optimal production plan?


So far, I've done work to this point and am stuck at what to do next..


Please help guide me in the right direction!

Thank you so much.

 

[Deleted member 4993]

Production plan for softdrinks​

Irene Martin works in a juice firm and has to develop the production plan for the lemon and the orange juice concentrates. The fruits (lemon and orange) that she needs to make the juice are not the bottleneck but Irene is concerned about the other main ingredients that go into making the juice: a water-based solution, sugar, and a vitamin mix. Checking with the ERP system tells her that she has 10900 kg of the water solution, 2970 kg of sugar, and 1990 kg of vitamin mix. The recipe tells her to use 52 kg of water solution to make a metric ton of lemon drink and 75 kg of water solution to make a metric ton of orange drink. For the lemon drink she also needs 24 kg of sugar and 17 kg of vitamin mix. The orange drink needs 11 kg of sugar and 7 kg of vitamin mix.
From the sales department, Ina knows that the lemon soft drink sells at 58 SEK/ton and the orange drink sells at 74 SEK/ton. (SEK = Swedish krona).

1) How much lemon drink should Irene produce to maximize revenue?

2) How much orange drink should Irene produce to maximize revenue?

3)How much revenue can Irene generate with the optimal production plan?


So far, I've done work to this point and am stuck at what to do next..
View attachment 28195

Please help guide me in the right direction!

Thank you so much.

Now assume that L tons of lemon drinks and R tons of orange drink have been produced

Write the cost function, the revenue function and the profit function for the production. Assign domain of L and R from the given constraints.

 

[JeffM]

Another bad, terrible, very not good problem. It has confused even the great Khan.

They have tried to make the problem look very realistic with terms like “ERP system.” But no one in real life except the most devout believer in central planning would ever ask such a question because it ignores costs (even Marx understood that things have costs; he just called them “social costs” to contrast them with what he considered the distorted costs inherent in capitalism.) The problem simply asks you to maximize revenue without any recognition of costs.

I suspect this problem came up in an effort to explain linear programming using super-simplified examples. If that is a correct guess, how have they taught you to do linear programming problems. If it is an incorrect guess, please say so, and we can help you from basic principles.