Suppose you have to prepare the color baths for Product A and Product B at the same time. How many liters of color bath for Product A and Product B can you prepare using the available inventory of the color blue and the UV agent?

P =     51.0 L Blue + 173.2 L UV

Q = 338.9 L Blue + 369.8 L UV

Explanation:

Each litre of blue colour contains 0.14 L P and 0.407 L Q.

Each litre of UV agent contains 0.475 L P and 0.444 L Q.

You have 390 L blue colour and 543 L of UV agent and must make the maximum amount of P and Q.

This gives you two simultaneous equations:  

1. Calculate P and Q

P = 364.7 L and Q = 832.8 L

2. Composition of P and Q

P will contain

0.14 × 364.7 L Blue + 0.475 × 364.7 L UV = 51.0 L Blue + 173.2 L UV

Q will contain  

0.407 × 832.8 L Blue + 0.444 × 832.8 L UV = 338.9 L Blue + 369.8 L UV

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answer; whoever is willing and able to pay the price;