Problem $1$: LP Modeling $$ MMA Auto Inc.

MMA Auto Inc., a world$-$renowned automotive manufacturer, specializes in two types of high$-$ performance truck models: the TerraMaster T$1$ and the AquaGlide A$2.$ The manufacturing process of the company is divided into three essential stages: engine assembly, painting, and quality control.

Here's the breakdown of each station's daily capacity:

$$ The engine assembly station could assemble $500$ TerraMaster T$1$ trucks if the engine assembly station were completely devoted to assembling TerraMaster T$1,$ or $450$ AquaGlide A$2$ trucks if the station were completely devoted to assembling AquaGlide A$2.$

$$ The painting station could paint $400$ TerraMaster T$1$ trucks if the paint shop were completely devoted to painting TerraMaster T$1,$ or $750$ AquaGlide A$2$ trucks if the shop were completely devoted to painting AquaGlide A$2.$

$$ The quality control station could inspect $750$ TerraMaster T$1$ trucks if the quality control station were completely devoted to inspecting TerraMaster T$1,$ or $600$ AquaGlide A$2$ trucks if the station were completely devoted to inspecting AquaGlide A$2.$

$$ The stations are flexible and can work on both models simultaneously.

Each TerraMaster T$1$ truck sold contributes $$1100$ to MMA Auto Inc.$\text{'}$s profit, while each AquaGlide A$2$ truck contributes $$1600.$ However, the company adheres to a policy to ensure product diversity and wants at least $30\%$ of the total production to be of the lesser$-$produced truck model.

Your task is to formulate a linear programming model to assist MMA Auto Inc. in determining the optimal quantity of each truck model to manufacture. The aim is to maximize their profit while considering the capacity constraints of the assembly, painting, and quality control stages, and the company's diversity policy.