Let the production function of a firm be `Q=5L^(1//2)K^(1//2)` . Find the maximum possible output that the firm can produce with 100 units of L and 100 units of K.

A firm produces x units of a product. The cost function C(x) and revenue function R(x) of x unit are given by C(x)=4(x+200) and R(x)=8(x+55). Find the minimum number of product the firm must produce the firm must produce to run as a profitable concern.

Manager of oil refinery wants to decide on the optional mix of two possible blending processes 1 and 2 of which the inputs and outputs per production run are as follows: The maximum amounts available of Crudes A and B are 200 units and 150 units respectively. At least 100 units of Gasoline X and 80 units of Y are required. The profit per production run from processes 1 and 2 are Rs. 3000 and Rs. 4000 respectively. Formulate the above as L.P.P.

A firm produces 3 products X,Y and Z requiring minimum of three materials A,B and C. The per unit requirement of material are given below. Using matrix notation determine (a) Production of each product if firm has 2900,1100 and 1450 units of each material respectively. (b) Total requirement of each material if the firm produces 200,300 and 100 units of the three products respectively.