Suppose that a firm wishes to fill an order for 2000 units of a product (i.e., the firm needs to produce 2000 units). The firm can produce the output at either one of two plants, the Tampa Plant and the Jacksonville Plant.

Let x = the output at the Tampa Plant, and y = the output at the Jacksonville. The firm's total cost function is given by c (x, y) = 2x^2 + xy +y^2 . Suppose that the firm wants to minimize the cost of producing the 2000 units. How should the production of the output be distributed between the two plants in order to minimize cost? please show your work