Suppose a Corporation Manufactures Candles at Two Locations $C _ { 2 } = 0.05 x _ { 2 } ^ { 2 } + 4 x _ { 2 } + 400$

Multiple Choice

Suppose a corporation manufactures candles at two locations. The cost of producing $x _ { 1 } \text { units at location } 1 \text { is } C _ { 1 } = 0.06 x _ { 1 } ^ { 2 } + 4 x _ { 1 } + 500 \text { and the cost of producing } x _ { 2 } \text { units at location } 2 \text { is }$ $C _ { 2 } = 0.05 x _ { 2 } ^ { 2 } + 4 x _ { 2 } + 400$ . The candles sell for $\$ 43$ per unit. Find the quantity that should be produced at each location to maximize the profit $P = 43 \left( x _ { 1 } + x _ { 2 } \right) - C _ { 1 } - C _ { 2 }$ .

A) $x _ { 1 } = 345 ; x _ { 2 } = 380$
B) $x _ { 1 } = 325 ; x _ { 2 } = 390$
C) $x _ { 1 } = 315 ; x _ { 2 } = 408$
D) $x _ { 1 } = 390 ; x _ { 2 } = 325$
E) $x _ { 1 } = 408 ; x _ { 2 } = 315$