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) $\$ 16,450$

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The Answer of 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) $\$ 16,450$

A Firm's Weekly Profit (In Dollars) in Marketing Two Products P=192x1+576x2−x12−5x22−2x1x2−5000P = 192 x _ { 1 } + 576 x _ { 2 } - x _ { 1 } ^ { 2 } - 5 x _ { 2 } ^ { 2 } - 2 x _ { 1 } x _ { 2 } - 5000P=192x1​+576x2​−x12​−5x22​−2x1​x2​−5000

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