### 7.1.1. Optimal Production Task

For the production of two types of products I and II, three types of raw materials are used.

To produce one unit of product I, it is required to spend 13 kg of the first type of raw material, 32 kg of the second type of raw material, and 58 kg of the third type of raw material.

To produce one unit of product II, it is required to spend 24 kg of the first type of raw material, 32 kg of the second type of raw material, and 29 kg of the third type of raw material.

The production is supplied with 312 kg of the first type of raw material, 480 kg of the second type of raw material, and 696 kg of the third type of raw material.

The profit from the sale of one unit of finished product I is 4 conditional units, and for product II - 3 conditional units.

It is required to develop a production plan for products I and II that ensures maximum profit from their sale, if it is planned in advance to produce at least 10 units of products I and II.