You are going to make and sell bread. a loaf of irish soda bread is made with 2 c flour and 1/4 c sugar. kngelhopf cake is made with 4 c flour and 1 c sugar. you will make a profit of $1.50 on each loaf of irish soda bread and a profit of $4 on each kugelhopf cake. you have 16 c flour and 3 c sugar. a.) how many of each kind of bread should you make to maximize the profit? b.) what is the maximum profit? show the formulas .

A)  You should make 4 loaf of Irish soda bread and 2 Kugelhopf cake to maximize the profit.

B)  The maximum profit is $14.

Explanation

Suppose, you should make loaf of Irish Soda Bread and loaf of Kugelhopf cake.

A loaf of Irish soda bread is made with 2 c flour and 1/4 c sugar. So, the amount of flour in loaf of bread is c and the amount of sugar is c.

Kngelhopf cake is made with 4 c flour and 1 c sugar. So, the amount of flour in loaf of bread is c and the amount of sugar is c.

You have total 16 c flour and 3 c sugar. So, the constraints will be.......

You will make a profit of $1.50 on each loaf of Irish Soda Bread and a profit of $4 on each Kugelhopf cake. So, the profit function will be:  

If we graph the above constraints, then the vertices of the common shaded region will be:   and  (Please refer to the below image for the graph)

For ,  

For ,  

For ,  

For ,  

So, the profit will be maximum, when   and

Thus, you should make 4 loaf of Irish soda bread and 2 Kugelhopf cake to maximize the profit.

The maximum profit will be $14

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

step-by-step explanation: