The Hardgrave Machine Company produces computer components at its plants in Kingston, ON; Prince George, BC; and Sudbury, ON. These plants supply the demand for orders at Hardgraves two warehouses in Hamilton and Regina.

The tables below present the information of: (i) the production cost and capacity for each of the three (3) plants, and the demand at each of the two warehouses

Production Plant	Monthly Supply (units)	Production Cost per Unit ($)
Kingston	15,000	$50
Prince George	20,000	$55
Sudbury	25,000	$45

Warehouse	Monthly Demand (Units)
Hamilton	35,000
Regina	30,000

Transportation costs per unit from each plant to each warehouse are summarized in the following table:

To: From:	Hamilton	Regina
Kingston Prince George Sudbury	$10 $25 $15	$20 $30 $20

Recent regulations require that no more than 8,000 units are to be shipped from the plant in Kingston to the Warehouse located in Hamilton. Also, at least 30% of the total computer components shipped to the warehouse in Regina are from the plant in Prince George.

Formulate algebraically the above problem to help Hardgrave satisfy the demand at the warehouses at the lowest production and transportation costs. Define the decision variables, objective function, and constraints. DO NOT SOLVE.