Bakery Pastry Production Analysis

A small bakery produces two types of pastries: croissants and muffins. The bakery has a daily production capacity of 200 pastries. The cost to produce a croissant is $1.50 and the cost to produce a muffin is $1.00. The bakery plans to maximize its profit, with croissants sold at $3.00 each and muffins at $2.00 each. If the bakery makes a profit of $150 in a day, how many croissants did it produce that day?

Let x represent the number of croissants and y the number of muffins produced.

Based on the bakery's constraints, set up the following system of equations:

1. Total production: $$ x + y = 200 $$

2. Total profit: $$ 3x + 2y - (1.5x + 1.0y) = 150 $$