The Chris Beehner Company manufactures two lines of designer yard gates, called model A and model B$.$ Every gate requires blending a certain amount of steel and zinc; the company has available a total of $25,000$ lb of steel and $6,000$ lb of zinc. Each model A gate requires a mixture of $125$ lb of steel and $20$ lb of zinc. Retail on model A gate is $$355,$ the expense to manufacture the gate is $$240.$ Each model B gate requires $100$ lb of steel and $30$ lb of zinc. Retail on model B gate is $$445,$ the expense to manufacture the gate is $$340.$ Additionally, the company is committed to manufacture at least $160$ model B gates.

Using Linear Programming, find the best production mix of yard gates.

a$.$ Number of model A gates to be produced $=$

$200$

b$.$ Number of model B gates to be produced $=$

$200$

c$.$ Chris Beehner's profit $=$ $

$[$ Select $]$

d$.$ Amount of unused steel $=$

$[$ Select $]$

lb

e$.$ Amount of unused zinc $=$

$[$ Select $]$

lb

f$.$ What if Beehner decided to increase the amount of zinc by $120$ lbs$,$ what impact would it have on profit?