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.
