Answer:
1240 widgets
Step-by-step explanation:
<em>The value of the function at 870, the local maximum, is
</em>
<em>= -0.02(870)2 + 34.80(870) - 4700
</em>
<em>= -0.02(756900) + 30276 - 4700
</em>
<em>= -15138 + 25576
</em>
<em>= 10438
</em>
<em> </em>
<em>So the vertex is (870, 10438)
</em>
<em> </em>
<em>The cost t the company to produce 870 widgets is </em>
<em>C(870) = 4700 + 5.20(870) = 4700 + 4524 = 9224
</em>
<em> </em>
<em>So, the cost of the widgets plus the profit must be equal to the total sales, which is divided by the number of widgets reveal their individual price.
</em>
<em>(10438 + 9224)/870 = 19662/870 = $22.60
</em>
<em> </em>
<em>P(x) = 7700
</em>
<em>- 0.02x2 + 34.80x - 4700 = 7700
</em>
<em>-0.02x2 + 34.80x -12400 = 0
</em>
<em> </em>
<em>x = {-34.80 ± √[(34.80)2 - 4(-0.02)(-12400)]}/2(-0.02)
</em>
<em>x = [-34.80 ± √(1211.04 - 992)]/(-0.04)
</em>
<em>x = (-34.80 ± √219.04)/(-0.04)
</em>
<em>x = (-34.80 ± 14.8)/(-0.04)
</em>
<em>x = 870 ± 370
</em>
<em>so, $7700 in profits will be earned at either 500 widgets or </em><em>1240 widgets</em>
