Answer :
The winery should set the prices of white wine and red wine at 4.5 Euros and 5.5 Euros respectively to maximize income, taking into account all constrains.
This problem is about maximizing profit and can be solved using linear programming. Let's denote the retail price of a bottle of white wine as x Euros and the retail price of a bottle of red wine as y euros. According to the provided information, we have the following constraints: x >= 3, y >= 4, 2x + y <= 15 and x + y <= 10.
To achieve maximum income, higher prices within the constraints are preferable. However, for the second constraint, if we set the price of 2 white wines at maximum i.e., 15 Euros, the price of a bottle of red wine would become zero, which invalidates the constraint y>=4. Similarly, we can't set the price of a white wine bottle at maximum (10 Euros) because then the price of red wine will be zero (invlidating y>=4).
Therefore, to meet all constraints, a price close to the maximum is prefered. Hence, the winery should set the price of white wine at 4.5 Euros and the price of red wine at 5.5 Euros. This way, the total cost of 2 bottles of white and one of red becomes 4.5*2+5.5=14.5 Euros, and the total cost of a bottle each of white and red becomes 4.5+5.5=10 Euros.
The answer is that the winery should set the prices of white wine at 4.5 Euros and red wine at 5.5 Euros to maximize their income. The explanation involves setting up and solving inequalities. The calculation involves simple arithmetic and considering economic logic to arrive at the solution.
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