State the KKT conditions for the problem and indicate whether they are necessary and / or sufficient.
A strawberry growing company is deciding its production and sale plan for the national and international markets.
The sale price for each ton of strawberry depends on the quantity offered in the market. If x1 tons is offered for the domestic market, the sale price will be (30 - x1) CU / ton, while if x2 tons is offered for the international market, the sale price will be (40 - x2) CU / ton.
The cost for each ton of strawberry for the domestic market is 10 MU, while for the international market it is 15 MU.
The company has the capacity to produce up to 10 tons of strawberries for sale and, according to SAG restrictions, it must dedicate at least 10% of its production to the international market.
For technical production reasons, the company must additionally satisfy the following restriction: x12 + x22 ≤64.
b) State the KKT conditions for the problem and indicate whether they are necessary and / or sufficient.
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