Question $5$

$\frac{0}{1}$ pt $9$

$(1)$ Details

A firm manufactures a commodity at two different factories, Factory $x$ and Factory $Y.$ The total cost $($in dollars$)$ of manufacturing depends on the quantities, $x$ and $y$ produced at each factory, respectively, and is expressed by the joint cost function:

$C(x,y)=x^2+xy+4y^2+1200$

A$)$ If the company's objective is to produce $1,200$ units per month while minimizing the total monthly cost of production, how many units should be produced at each factory? $($Round your answer to whole units, $i.$e$.$ ne decimal places.$)$

To minimize costs, the company should produce:

units at Factory $x$ and

units at Factory $Y$

B$)$ For this combination of units, their minimal costs will be enter any cornmas in your answer.$)$ dollars. $($Do not

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