Maximizing Type A Bicycles

A manufacturer produces two types of bicycles, type A and type B. The cost to produce one bicycle of type A is $75, while the cost for type B is $100. The manufacturer has a budget of $4500 for the production of the bicycles. Let a represent the number of type A bicycles produced and b denote the number of type B bicycles produced.

The manufacturer aims to produce at least 30 bicycles in total. Therefore, the following conditions must be satisfied:

• $$ 75a + 100b \\leq 4500 $$
• $$ a + b \\geq 30 $$

What is the maximum number of type A bicycles that can be produced while still satisfying both conditions?