CanZinc Company specializes in the mining and refining of rough zinc. The company mine rough zinc from mine A and mine B. The company refines the rough zinc in plant 1 and plant 2. A few weeks ago Canzinc received an order of 12,000 tons of refined zinc. To fill this order, Canzinc started mining from tow new mines; mine c and mine D. The following data shows the mining capacity for each mine and the grade of zinc produced in refining. The grade of Zinc represents the volume of refined zinc that can be obtained with 1 ton of rough zinc

Mine	Maximum capacity	Grade of Zinc per ton of rough zinc
A	9,000 tons	0.40 per ton
B	8,000 tons	0.35 per ton
C	6,000 tons	0.50 per ton
D	10,000 tons	0.40 per ton

Plant 1 can refined 15,000 tons and plant 2 can refine 17,000 tons

The controller of CanZinc wants to minimize the cost of transportation of the rough zinc. He has determined the costs of transportation per ton between the four mines and two plants as follows:

Mine	Plant 1	Plant 2
A	$20	$15
B	$30	$30
C	$35	$25
D	$40	$45

a) Formulate the above as a linear program to minimize the cost of transportation.