A Manufacturer Has an Order for 1100 Units of Fine $x _ { 1 }$

Multiple Choice

A manufacturer has an order for 1100 units of fine paper that can be produced at two locations. Let $x _ { 1 }$ and $x _ { 2 }$ be the numbers of units produced at the two plants. Find the number of units that should be produced at each plant to minimize the cost if the cost function is given by $C = 0.2 x _ { 1 } ^ { 2 } + 25 x _ { 1 } + 0.05 x _ { 2 } ^ { 2 } + 12 x _ { 2 }$ .

A) $x _ { 1 } = 388$ units and $x _ { 2 } = 906$ units
B) $x _ { 1 } = 906$ units and $x _ { 2 } = 194$ units
C) $x _ { 1 } = 194$ units and $x _ { 2 } = 906$ units
D) $x _ { 1 } = 194$ units and $x _ { 2 } = 1812$ units
E) $x _ { 1 } = 1812$ units and $x _ { 2 } = 388$ units