Please show all formulas used. (This is the question in its entirety; Sorry, I don't have anything more to update :( )

A warehouse supplies goods to three customers, each of whom require 30 units. The company has two warehouses. In warehouse 1, 40 units are available, and in warehouse 2, 30 units are available. The costs of shipping one unit from each warehouse to each customer are shown. Also shown is a penalty for each unsatisfied customer unit of demand - with customer 1 a penalty cost of $90 is incurred; with customer 2 , the penalty is $80; and with customer 3 , the penalty is $110. How do we minimize the sum of penalty and shipping costs? How does a change in the unit penalty cost of customer 3 affect the optimal cost? How does a change in the capacity of warehouse 2 affect the optimal cost? A warehouse supplies goods to three customers, each of whom require 30 units. The company has two warehouses. In warehouse 1, 40 units are available, and in warehouse 2, 30 units are available. The costs of shipping one unit from each warehouse to each customer are shown. Also shown is a penalty for each unsatisfied customer unit of demand - with customer 1 a penalty cost of $90 is incurred; with customer 2 , the penalty is $80; and with customer 3 , the penalty is $110. How do we minimize the sum of penalty and shipping costs? How does a change in the unit penalty cost of customer 3 affect the optimal cost? How does a change in the capacity of warehouse 2 affect the optimal cost