A firm produces a good using two raw materials R1 and R2, and the corre- sponding costs per unit of these raw materials are $2 and $7 respectively. The amount of its good that a firm can produce using r units of R1 and y units of R2 is given by √x + √y. Use the method of Lagrange multipliers to find the optimal values of x and y that minimize the cost of the raw materials Ri and R2 which will enable the firm to produce a total amount q0 of its good.