Using the same process as in the discussion question, cookie example we did in class, please identify the following so we can use it in class when we move to graphing.

$1.$ Identify the variables $($unknowns$)$

$2.$ Write the Objective Function

$3.$ Identify and formulate the constraints

$4.$ Write the feasible solutions that represent the constraints including non$-$negative restriction and then using the constraint formulas above, identify the coordinates we will use to graphically represent the constraints.

Problem $1$: LOGISTICS $(5$ points$)$

A school is preparing a trip for $400$ students. The company who is providing the transportation has $10$ buses of $50$ seats each and $8$ buses of $40$ seats, but only has $9$ drivers available. The rental cost for a large bus is $$800$ and $$600$ for a small bus. Calculate how many buses of each type should be used for the trip for the least possible cost.

Problem $2$: PROMOTONAL SALES $(5$ points$)$

A store wants to liquidate $200$ shirts and $100$ pairs of pants from last season. They have decided to put together two offers, A and B$.$ Offer A is a package of one shirt and a pair of pants which will sell for $30.$ Offer B is a package of three shirts and a pair of pants, which will sell for $50.$ The store does not want to sell less than $20$ packages of Offer A and less than $10$ of Offer B$.$ How many packages of each do they have to deal to maximize the money generated from the promotion?