The optimization problem is the hint to the main solustion.

I would appreciate having a solution written with nice handwriting and detail explanations.

A rm can produce its product in two plants. The cost of producing output qi in Plant 3' is %ciq-2 for some positive constant (33-. In addition, Plant 2' can produce at most (j;- output. The market price of the product is (1 q1 92) Where (q1 + (12) is the total output. Find the rm's optimal production plan. Ignore the transportation cost. Solution. We solve the following program: 1 1 maxq1,Q2 (91 + (D)\" * 9'1 \" (12) * $3191 r C2Q; Si. (115 S (15, for Z : 1,2