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 q₂are 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?

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The Answer of 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 q₂are 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?

A Company Has Two Manufacturing Plants Which Manufacture the Same C(q1,q2)=4q12+q1q2+q22C \left( q _ { 1 } , q _ { 2 } \right) = 4 q _ { 1 } ^ { 2 } + q _ { 1 } q _ { 2 } + q _ { 2 } ^ { 2 }C(q1​,q2​)=4q12​+q1​q2​+q22​

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