2) Donut Delights, Inc. has determined that when x donuts are made daily, the pr

Question

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

(a) What is the company’s profit if 700 donuts are made daily?

(b) How many donuts should be made daily in order to maximize the company’s profit? Show work.

3) A salesperson earns a base salary of $1,560 per month and a commission of 7.8% on the amount of sales. If the salesperson has a paycheck of $4,543.50 for one month, what was the amount of sales for the month? Show work.

4)  Find the equation for a line which passes through the points (5, 2) and (7, –8). Write the equation in slope-intercept form. Show work.

Explanation / Answer

1. 5x^2 = 6x + 3

subtract 6x from both sides

5x^2 -6x

subtract 3 from both sides

5x^2 -6x - 3 = 0

applying quadratic formula to solve

x = { -b + - sqrt(b^2 -4ac) } /2a

a = 5 , b=-6 , c = -3

plugging the values we get

x = {3 +- 2sqrt 6} / 5

1st solution is x = {3 + 2 sqrt 6 } / 5

2nd solution is x =   {3 - 2 sqrt 6 } / 5

2) p(x) = -.002x^2 +4.7x -135

a) if 700 donuts are made daily (plug x = 700)

p(700) = -.002*700^2 +4.7*700 -135 = -980 + 3290 - 135 = 2175

profit is $ 2175

b) to maximize the profit donuts should be -b/2a

b = 4.7 , a = -.002

donuts = -4.7 / 2*-.002 = 1175

therefore 1175 donuts should be made to maximize the profit

4) two points are (5,2) and (7,-8 )

slope = y2-y1/x2-x1 = -5

therefore slope intercept form is

y = mx + b

taking a point (5,2)

2 = -5*5 + b

b = 27

y = -5x + 27

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