SOLUTION: sammy is selling widgets. If he sells 1 widget, it costs him $1 to produce it and he can sell it for $10. If he sells 2 widgets, it costs him $2 to produce 2 widgets, but he can on
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Question 1206524: sammy is selling widgets. If he sells 1 widget, it costs him $1 to produce it and he can sell it for $10. If he sells 2 widgets, it costs him $2 to produce 2 widgets, but he can only get $9 for each widget. It costs $1 to produce each widget. The average price decreases by $1 for every extra widget sold. How many widgets should sammy sell to maximise his profit? Answer by ikleyn(52782) (Show Source):
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sammy is selling widgets. If he sells 1 widget, it costs him $1 to produce it and he can sell it for $10.
If he sells 2 widgets, it costs him $2 to produce 2 widgets, but he can only get $9 for each widget.
It costs $1 to produce each widget. The average price decreases by $1 for every extra widget sold.
ow many widgets should sammy sell to maximise his profit?
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Cost producing x widgets is x dollars.
Selling price of each one widget in the group of x widgets is 11-x.
So the profit is
P(x) = Revenue(x) - Cost(x) = x*(11-x) - x = -x^2 + 10x.
The maximum of P(x) is at = " ", where "a" is the coefficient
at , "b" is the coefficient at x.
In this problem, = = = 5.
So, the optimum number of widgets in group to produce and to sell is 5.
It gives the maximum profit of -5^2 + 10*5 = -25 + 50 = 25 dollars per group.
