A Firm's Weekly Profit (In Dollars) in Marketing Two Products $P = 192 x _ { 1 } + 576 x _ { 2 } - x _ { 1 } ^ { 2 } - 5 x _ { 2 } ^ { 2 } - 2 x _ { 1 } x _ { 2 } - 5000$

Multiple Choice

A firm's weekly profit (in dollars) in marketing two products is given by $P = 192 x _ { 1 } + 576 x _ { 2 } - x _ { 1 } ^ { 2 } - 5 x _ { 2 } ^ { 2 } - 2 x _ { 1 } x _ { 2 } - 5000$ where $x _ { 1 }$ and $x _ { 2 }$ represent the numbers of units of each product sold weekly. Estimate the average weekly profit when $x _ { 1 }$ varies between 40 and 50 units and $x _ { 2 }$ varies between 45 and 50 units.

A) $\$ 12,300$
B) $\$ 11,100$
C) $\$ 13,400$
D) $\$ 21,760$
E) $\$ 16,450$