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1)Donut Delights, Inc. has determined that when x donuts are made daily, the profit P is given by
 
P(x)=-0.002x2+4.3x-130
 
a) How is the company's profit if 700 donuts are mad daily?
b) How many donuts should be made daily in order to maximize the company's profit show work.
 
2) A salesperson earns a base salary of $2,100 per month and a commission of 5.8% on the amount of sales made. If the sales person has a paycheck of $3,764.60 for one month. What was the amount of sales for the month? show work.
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1 Answer

1)Donut Delights, Inc. has determined that when x donuts are made daily, the profit P is given by

P(x)=-0.002x2+4.3x-130

a) How is the company's profit if 700 donuts are mad daily?
 
Plug x=700 into the P(x) equation
P(700) = -0.002(7002) + 4.3(700) - 130
 
b) How many donuts should be made daily in order to maximize the company's profit show work.
 
The equation for P is a quadratic equation, so its graph is a parabola.  Since the coefficient of the x2 term is negative (-0.002), it's an upside down parabola with the vertex at the top.  The vertex, then, will be the maximum value for P(x).  The x coordinate of the vertex is (-b/2a) where a=(-0.002) and b=4.3.  Plug that value of x into the P(x) equation to get the maximum profit.
 
2) A salesperson earns a base salary of $2,100 per month and a commission of 5.8% on the amount of sales made. If the sales person has a paycheck of $3,764.60 for one month. What was the amount of sales for the month? show work.
 
Let x = the amount of sales per month (in $$)
Let y = the Salesperson's salary for the month
 
y = (0.058)x + 2100     [If x=0, y=2100, the base salary.  0.058 is the decimal equivalent of 5.8%]
 
To find the amount of sales in the month, plug in the value of the salesperson's salary for the month:
 
3764.60 = (0.058)x + 2100
 
Solve for x.