$1.$ Formulate a linear programming model for this problem.

$2.$ What is the optimal solution to the problem?

$3.$ What is the allowable increment and decrement $($kg$)$ for animal protein? Explain the effect on objective function if the optimal decision variable value is changed between the range.

$4.$ What is the allowable increment and decrement $($kg$)$ for carbohydrates? Explain the effect on objective function if the right$-$hand side value is changed between the range.

$5.$ If the mixture of the fish feed is $1$kg of animal protein, $2$kg of yellow corn and $2$kg of soy flour. Please state whether the solution is feasible or not. If so$,$ what is the daily cost for this ingredient?

$6.$ The mixture of the fish feed is proposed as $1$kg of animal protein, $1$kg of yellow corn and $2$kg of soy flour. Please state whether the solution is feasible or not. Explain. Please answer all question with working breakdown