Assume that we are trying to create a mixture for feeding the animals in a farm. In that mixture we can use two types of ingredients, ingredient 1 and ingredient 2. The mixture should meet some desired levels for two types of chemicals, chemical A and chemical B. One bag of ingredient 1 contributes 4 units to chemical A and 10 units of chemical B. Similarly, one bag of ingredient 2, contributes 8 units of chemical A and 2 units of ingredient 2. The desired levels for chemical A and chemical B should be at least 40 and 20 units, respectively. Due to some market restrictions, we cannot buy more than 8 bags of ingredient 1. Unit price of one bag ingredient 1 and ingredient 2 are $3 and $4, respectively. Determine the number of bags of ingredient 1 and ingredient 2 to purchase to minimize the cost. a) Formulate a linear programming model for this problem. (50pts) b) Solve this model by using graphical analysis. (50pts)