Answer to Question #293439 in Linear Algebra for abeni

Question

3. A firm can produce a good either by (i) a labor intensive technique, using 8 units of labor and 1 unit of capital or (ii) a capital intensive technique using 1 unit of labor and 2 units of capital. The firm can arrange up to 200 units of labor and 100 units of capital. Note that the firm produce goods X and Y in process land 1 and 2 respectively. Its objective is to maximize profit by selling the good.

i) Construct the objective function and the constant inequalities.

ii) By drawing the graphs of the linear constraints, find the optimal solutions.

 iii) Find the solution using the simplex methods.