In: Operations Management
The Nutmeg Corporation produces three different? products, each in a? 1-pound can:? Almond-Lovers Mix,? Walnut-Lovers Mix, and Thrifty Mix. Three types of nuts are used in? Nutmeg's products:? almonds, walnuts, and peanuts. Nutmeg currently has 400 pounds of? almonds,200pounds of? walnuts, and 1,000 pounds of peanuts. Each of? Nutmeg's products must contain a certain percentage of each type of? nut, as shown in the following table. The table also shows the revenue per can as well as the cost per pound to purchase nuts.
Percentage Requirements per Can |
||||
Almonds |
Walnuts |
Peanuts |
Revenue per can |
|
?Almond-Lovers Mix |
70?% |
30?% |
0?% $8.00 |
|
?Walnut-Lovers Mix |
30?% |
70?% |
0?% |
?$10.00 |
Thrifty Mix |
10?% |
10?% |
80?% |
?$4.50 |
Cost per pound |
?$3.50 |
?$7.00 |
?$3.00 |
a. Given? Nutmeg's current stock of? nuts, how many cans of each product should be produced to maximize? revenue?
Decision? variables:
X1
? = number of cans of? Almond-Lovers Mix to be produced
X2
? = number of cans of? Walnut-Lovers Mix to be produced
X3
? = number of cans of Thrifty Mix to be producedObjective? function: Maximize
Zequals=nothingX1plus+nothingX2plus+nothingX3
. ?(Enter your responses rounded to two decimal? places.)
?Constraints: ?(Enter your responses for the coefficients rounded to two decimal? places.)
Almonds
?(C1?) |
nothingX1plus+nothingX2plus+nothingX3
? greater than or equals? less than or equals? equals= greater than> less than< nothing |
Walnuts
?(C2?) |
nothingX1plus+nothingX2plus+nothingX3
? greater than or equals? equals= less than or equals? less than< greater than> nothing |
Peanuts
?(C3?) |
nothingX1plus+nothingX2plus+nothingX3
? less than or equals? equals= less than< greater than> greater than or equals? nothing |
?Nonnegativity: |
X1?, X2?, X3greater than or equals?0 |
A linear programming software shows the optimal solution? as:
X1equals=250250?,
X2equals=00?,
What is the optimal value for
X3??
X3equals=nothing.
?(Enter your response rounded to the nearest whole? number.)b. Does the solution you developed in part? (a) change if Nutmeg is interested in maximizing contribution margin? (defined as revenue per unit
minus?
raw material? cost)?
First modify the objective function. ?(Enter your responses rounded to two decimal? places.)
Maximize
Zequals=nothingX1plus+nothingX2plus+nothingX3
A linear programming software shows the optimal solution? as:
X1equals=500500?,
X2equals=00?,
What is the optimal value for
X3??
X3equals=nothing.
?(Enter your response rounded to the nearest whole? number.)c. If
100100
additional pounds of walnuts became? available, how would your? contribution-margin maximizing solution from part? (b) change?
A.
The optimal value for
X1?,
the number of cans of? Almond-Lovers Mix to be? produced, would
decreasedecrease.
B.
The optimal value for
X3?,
the number of cans of Thrifty Mix to be? produced, would
decreasedecrease.
C.
The optimal value for
X2?,
the number of cans of? Walnut-Lovers Mix to be? produced, would decrease.
Click to select your answer(s).
a)
It is a linear programming problem which can be solved in excel as below
Then go to the data tab and click on solver and put the constraints and objective function as below
Then click on solve and keep solver solution
thus 250 Almond lovers mix and 1250 Thrifty mix to be produced to maximize revenue
b)
Repeat the steps in a except that objective function would now be to maximixe contribution margin instead of revenues
thus now
500 Almond lovers mix and 500 Thrifty mix to be produced to maximize margin
c)
repeat the steps in optio b with one constraint changed which is walnuts available
and the ouput would be
thus X1 has decreased
X 2 has increased
X3 has increased