A Company Has Two Manufacturing Plants Which Manufacture the Same $C \left( q _ { 1 } , q _ { 2 } \right) = 4 q _ { 1 } ^ { 2 } + q _ { 1 } q _ { 2 } + q _ { 2 } ^ { 2 }$

Essay

A company has two manufacturing plants which manufacture the same item.Suppose the cost function is given by $C \left( q _ { 1 } , q _ { 2 } \right) = 4 q _ { 1 } ^ { 2 } + q _ { 1 } q _ { 2 } + q _ { 2 } ^ { 2 }$ where q₁ and q₂ are the quantities (measured in thousands)produced in each plant.The total demand q₁ + q₂ is related to the price, p, by $p = 110 - 0.5 \left( q _ { 1 } + q _ { 2 } \right)$ How much should each plant produce in order to maximize the company's profit?