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, I and y, produced at each factory, respectively, and
is expressed by the Joint cost function:
C(x, y) = 5x2 + 4xy + 6y? +3000
A) If the company manufactures 110 units at Factory X and 170 units at Factory Y, what are the total costs
of production?
Total Costs = 5
B) Find an expression for the rate of change of costs with respect to units produced at Factory X. Write
your answer as an expression, not an equation (1.e. do not use an = sign).
Your expression -
C) Find an expression for the rate of change of costs with respect to units, produced at Factory Y. Write your
answer as an expression, not an equation (ie, do not use ansign).
Your expression
D) Find the rate of change of costs with respect to units produced at Factory. X when 110 units have been
produced at Factory X and 170 units have been produced at Factory Y.
Rate of change
dollars per unit produced at X.
E) Find the rate of change of costs with respect to units produced at Factory Y when 110 units have been
produced at Factory X and 170 units have been produced at Factory Y.
Rate of change -
dollars per unit produced at Y.