The Lake District Tea Company produces two blends of tea: Windermere Strong Blend, which it sells for $14$ per kg$,$ and Buttermere Delicate Blend, which it sells for $15$ per kg$.$ Both of these blends are produced by mixing two types of leaves: Assam leaves, which cost $9$ per kg$,$ and Kenyan tea leaves, which cost $12$ per kg$.$ Windermere Strong Blend is made from $70\%$ Assam tea leaves and $30\%$ Kenya tea leaves, while Buttermere Delicate Blend is made with $40\%$ Assam tea leaves and $60\%$ Kenyan tea leaves. The company expects to sell up to $20$kg of Windermere Strong Blend, and all of the Buttermere Delicate Blend that it produces. The company has a total of $100$ kg of each type of tea leaf available and would like to select the amount of each tea blend to produce to maximize its profits.