Not sure if I came to the right place for this if not could someone
please direct me else where, but I've been trying to figure out these 2
problems below. If someone could help me out on where to get started, I
would be greatful. Thanks

1.A Blending Problem
Bryant's Pizza, Inc. is a producer of frozen pizza products. The
company makes a net income of $1.00 for each regular pizza and $1.50
for each deluxe pizza produced. The firm currently has 150 pounds of
dough mix and 50 pounds of topping mix. Each regular pizza uses 1 pound
of dough mix and 4 ounces (16 ounces= 1 pound) of topping mix. Each
deluxe pizza uses 1 pound of dough mix and 8 ounces of topping mix.
Based on the past demand per week, Bryant can sell at least 50 regular
pizzas and at least 25 deluxe pizzas. The problem is to determine the
number of regular and deluxe pizzas the company should make to maximize
net income. Formulate this problem as an LP problem.
Let X1 and X2 be the number of regular and deluxe pizza, then the LP
formulation is:
Maximize X1 + 1.5 X2
Subject to:
X1 + X2  150
0.25 X1 + 0.5 X2  50
X1  50
X2  25
X1  0, X2  0
NOTE: the boxes are greater then or equal too

2.A Product-Replacement Problem
A price-taking firm sells S units of its product at the market price of
p. Management's policy is to replace defective units at no additional
charge, on the first-come, first-served basis, while replacement units
are available. Because management does not want to risk making the same
mistake twice, it produces the units that it sells to the market on one
machine. Moreover, it produces the replacement units, denoted X, on a
second, higher-quality machine. The fixed cost associated with
operating both machines, the variable cost, and replacement cost are
given is the short-run cost function C(X) = 100 + 20S + 30X.
The exact probability that a unit will be defective is r. Acting out of
caution, however, management always underestimate the reliability of its
product. Nonetheless, it imposes the condition that X  r.S. The
demand for the firm's product is given by S(r) = 10000e-0.2r. Hence the
decision problem is to maximize the net profit function P(X):
Maximize P(X) = 100000p e- 0.2r - 100 - 20S - 30X,
subject to: X  r.S.
As we will learn, the solutions to the LP problems are at the vertices
of the feasible region. Therefore, the net profit P(X) will be
maximized if the management set X = r.S.
NOTE: the boxes are greater then or equal too

If anyone could help that would be great if not thank you for your
time.


--
ithebatman
------------------------------------------------------------------------
ithebatman's Profile: http://www.excelforum.com/member.php...o&userid=33996
View this thread: http://www.excelforum.com/showthread...hreadid=537601

This sounds like a student having trouble with classwork and using the NGs to solve his problems. You might get someone to do your
work for you here, but if you want to learn anything in school then you need to learn to do your own work and hammer these story
problems out on your own.

I already graduated. Not interested in more accounting courses for someone else's benefit.
--
RMC,CPA


"ithebatman" wrote in message
...

Not sure if I came to the right place for this if not could someone
please direct me else where, but I've been trying to figure out these 2
problems below. If someone could help me out on where to get started, I
would be greatful. Thanks

1.A Blending Problem
Bryant's Pizza, Inc. is a producer of frozen pizza products. The
company makes a net income of $1.00 for each regular pizza and $1.50
for each deluxe pizza produced. The firm currently has 150 pounds of
dough mix and 50 pounds of topping mix. Each regular pizza uses 1 pound
of dough mix and 4 ounces (16 ounces= 1 pound) of topping mix. Each
deluxe pizza uses 1 pound of dough mix and 8 ounces of topping mix.
Based on the past demand per week, Bryant can sell at least 50 regular
pizzas and at least 25 deluxe pizzas. The problem is to determine the
number of regular and deluxe pizzas the company should make to maximize
net income. Formulate this problem as an LP problem.
Let X1 and X2 be the number of regular and deluxe pizza, then the LP
formulation is:
Maximize X1 + 1.5 X2
Subject to:
X1 + X2  150
0.25 X1 + 0.5 X2  50
X1  50
X2  25
X1  0, X2  0
NOTE: the boxes are greater then or equal too

2.A Product-Replacement Problem
A price-taking firm sells S units of its product at the market price of
p. Management's policy is to replace defective units at no additional
charge, on the first-come, first-served basis, while replacement units
are available. Because management does not want to risk making the same
mistake twice, it produces the units that it sells to the market on one
machine. Moreover, it produces the replacement units, denoted X, on a
second, higher-quality machine. The fixed cost associated with
operating both machines, the variable cost, and replacement cost are
given is the short-run cost function C(X) = 100 + 20S + 30X.
The exact probability that a unit will be defective is r. Acting out of
caution, however, management always underestimate the reliability of its
product. Nonetheless, it imposes the condition that X  r.S. The
demand for the firm's product is given by S(r) = 10000e-0.2r. Hence the
decision problem is to maximize the net profit function P(X):
Maximize P(X) = 100000p e- 0.2r - 100 - 20S - 30X,
subject to: X  r.S.
As we will learn, the solutions to the LP problems are at the vertices
of the feasible region. Therefore, the net profit P(X) will be
maximized if the management set X = r.S.
NOTE: the boxes are greater then or equal too

If anyone could help that would be great if not thank you for your
time.


--
ithebatman
------------------------------------------------------------------------
ithebatman's Profile: http://www.excelforum.com/member.php...o&userid=33996
View this thread: http://www.excelforum.com/showthread...hreadid=537601

Look for solvsamp.xls distributed with office - probably in the
Examples\Solver subdirectory under Office.

--
Regards,
Tom Ogilvy


"ithebatman" wrote
in message ...

Not sure if I came to the right place for this if not could someone
please direct me else where, but I've been trying to figure out these 2
problems below. If someone could help me out on where to get started, I
would be greatful. Thanks

1.A Blending Problem
Bryant's Pizza, Inc. is a producer of frozen pizza products. The
company makes a net income of $1.00 for each regular pizza and $1.50
for each deluxe pizza produced. The firm currently has 150 pounds of
dough mix and 50 pounds of topping mix. Each regular pizza uses 1 pound
of dough mix and 4 ounces (16 ounces= 1 pound) of topping mix. Each
deluxe pizza uses 1 pound of dough mix and 8 ounces of topping mix.
Based on the past demand per week, Bryant can sell at least 50 regular
pizzas and at least 25 deluxe pizzas. The problem is to determine the
number of regular and deluxe pizzas the company should make to maximize
net income. Formulate this problem as an LP problem.
Let X1 and X2 be the number of regular and deluxe pizza, then the LP
formulation is:
Maximize X1 + 1.5 X2
Subject to:
X1 + X2  150
0.25 X1 + 0.5 X2  50
X1  50
X2  25
X1  0, X2  0
NOTE: the boxes are greater then or equal too

2.A Product-Replacement Problem
A price-taking firm sells S units of its product at the market price of
p. Management's policy is to replace defective units at no additional
charge, on the first-come, first-served basis, while replacement units
are available. Because management does not want to risk making the same
mistake twice, it produces the units that it sells to the market on one
machine. Moreover, it produces the replacement units, denoted X, on a
second, higher-quality machine. The fixed cost associated with
operating both machines, the variable cost, and replacement cost are
given is the short-run cost function C(X) = 100 + 20S + 30X.
The exact probability that a unit will be defective is r. Acting out of
caution, however, management always underestimate the reliability of its
product. Nonetheless, it imposes the condition that X  r.S. The
demand for the firm's product is given by S(r) = 10000e-0.2r. Hence the
decision problem is to maximize the net profit function P(X):
Maximize P(X) = 100000p e- 0.2r - 100 - 20S - 30X,
subject to: X  r.S.
As we will learn, the solutions to the LP problems are at the vertices
of the feasible region. Therefore, the net profit P(X) will be
maximized if the management set X = r.S.
NOTE: the boxes are greater then or equal too

If anyone could help that would be great if not thank you for your
time.


--
ithebatman
------------------------------------------------------------------------
ithebatman's Profile:
http://www.excelforum.com/member.php...o&userid=33996
View this thread: http://www.excelforum.com/showthread...hreadid=537601