FMGT 7210 - Class 3
Steps for solving optimization problems? - ANS-1) Identify the decision variables
2) Write objective function
3) Writing the constraints
4) Write the non-negativity restriction.
5) Solve graphically or with excel
what does identifying the decision variables consist of? - ANS-Must determine X and Y, what
you are trying to optimize. Such as total area for growing Wheat (X) and total area for growing
Barley (Y)
How do you write an objective function? - ANS-An objective function is a formula to maximize
profit. If a farmer gets a profit of $50 for X and $120 for Y and you are trying to determine how
much of each to make the formula would be :
Max Z= 50X +120Y
What is an objective function ? - ANS-The objective function is the mathematical representation
of the objective that you are solving. In this case, mathematically, how many hectares are
allocated to wheat (X) and barley (Y) respectively, to maximize profit (Z)?
How do you write the constraints? - ANS-You look at the restrictions the business has and put it
into an equation.
What is the constraint equation if:
It is given that the farmer has a total budget of $10,000. The cost of producing (100) wheat
(200) barley per hectare is given. - ANS-100X + 200Y <= 10,000
What is the constraint equation if:
there is a limited availability on the total number of worker-days for the planning horizon. The
total number of worker-days available are 1,200. We are given the worker-days per hectare for
(10) wheat and (30) barley. - ANS-10X + 30Y <= 1,200
What is the constraint equation if: • limited total area present for plantation. The total available
area is 110 hectares. - ANS-X + Y <=110
What is the non-negativity restriction? - ANS-It makes sure that the values of X and Y are
greater than or equal to 0.
What is the non-negativity restriction equation? - ANS-X>= 0, Y>=0
, How do you solve an optimization problem with a graph? - ANS-1) Write out all equations from
the first four steps and simplify them.
2) plot the equations on graph
How do you plot the equations on the graph? - ANS-Set Y to zero to determine the
corresponding X value and then by setting X to zero to determine the corresponding Y value. It
doesn't matter which order you plot the lines, just plot them all one by one.
How do you know what the optimal solution is after plotting an equation on the graph? -
ANS-The optimal solution will fall beneath the constraint line. After plotting all equations
optimization occurs where the sub-constraints intersect.
How do you solve an optimization problem with excel? - ANS-1) Identify the decision variables
and enter them in variable cells.
2) Write the objective function by copying the decision variable numbers in first row and cost
below. Calculate the total cost by using =Sumproduct (row1, row2)
3) Enter constraints in new table below. with total being =Sumproduct(row1 in objective, row of
constraint)
4) Enter information in the solver
How do you enter information in the excel solver - ANS-1) Set Objective is the cell you want to
maximize, minimize or set to a specific value
2) The variable cells in this case will be the quantity of each food item
3) The constraints can be added by selecting, "Add" to the right of the "Subject to the
Constraints" box
4) Make sure you select check "Make Unconstrained Variable Non-Negative"
5) The Solving Method is: Simplex LP
6) Click, "Solve"
7) Keep solver solution and select "OK" and you will see the variable cells have been changed
to what is now the optimal solution:
what is linear cost behaviour? - ANS-variable costs
y=mx
what is variable costs? - ANS-cost per unit multiplied by the number of units
What do we need to think about before we use a cost per unit? - ANS-must look at capacity (do
you have capacity to make more units), what is the relevant range in which we are operating (is
the range of production where variable cost per unit is true)
What are the non-linear cost behaviours? - ANS-fixed cost y=b and mixed cost y=mx +b
what are some examples of fixed cost? - ANS-raw materials, labour, salary potentially, rent or
lease costs
Steps for solving optimization problems? - ANS-1) Identify the decision variables
2) Write objective function
3) Writing the constraints
4) Write the non-negativity restriction.
5) Solve graphically or with excel
what does identifying the decision variables consist of? - ANS-Must determine X and Y, what
you are trying to optimize. Such as total area for growing Wheat (X) and total area for growing
Barley (Y)
How do you write an objective function? - ANS-An objective function is a formula to maximize
profit. If a farmer gets a profit of $50 for X and $120 for Y and you are trying to determine how
much of each to make the formula would be :
Max Z= 50X +120Y
What is an objective function ? - ANS-The objective function is the mathematical representation
of the objective that you are solving. In this case, mathematically, how many hectares are
allocated to wheat (X) and barley (Y) respectively, to maximize profit (Z)?
How do you write the constraints? - ANS-You look at the restrictions the business has and put it
into an equation.
What is the constraint equation if:
It is given that the farmer has a total budget of $10,000. The cost of producing (100) wheat
(200) barley per hectare is given. - ANS-100X + 200Y <= 10,000
What is the constraint equation if:
there is a limited availability on the total number of worker-days for the planning horizon. The
total number of worker-days available are 1,200. We are given the worker-days per hectare for
(10) wheat and (30) barley. - ANS-10X + 30Y <= 1,200
What is the constraint equation if: • limited total area present for plantation. The total available
area is 110 hectares. - ANS-X + Y <=110
What is the non-negativity restriction? - ANS-It makes sure that the values of X and Y are
greater than or equal to 0.
What is the non-negativity restriction equation? - ANS-X>= 0, Y>=0
, How do you solve an optimization problem with a graph? - ANS-1) Write out all equations from
the first four steps and simplify them.
2) plot the equations on graph
How do you plot the equations on the graph? - ANS-Set Y to zero to determine the
corresponding X value and then by setting X to zero to determine the corresponding Y value. It
doesn't matter which order you plot the lines, just plot them all one by one.
How do you know what the optimal solution is after plotting an equation on the graph? -
ANS-The optimal solution will fall beneath the constraint line. After plotting all equations
optimization occurs where the sub-constraints intersect.
How do you solve an optimization problem with excel? - ANS-1) Identify the decision variables
and enter them in variable cells.
2) Write the objective function by copying the decision variable numbers in first row and cost
below. Calculate the total cost by using =Sumproduct (row1, row2)
3) Enter constraints in new table below. with total being =Sumproduct(row1 in objective, row of
constraint)
4) Enter information in the solver
How do you enter information in the excel solver - ANS-1) Set Objective is the cell you want to
maximize, minimize or set to a specific value
2) The variable cells in this case will be the quantity of each food item
3) The constraints can be added by selecting, "Add" to the right of the "Subject to the
Constraints" box
4) Make sure you select check "Make Unconstrained Variable Non-Negative"
5) The Solving Method is: Simplex LP
6) Click, "Solve"
7) Keep solver solution and select "OK" and you will see the variable cells have been changed
to what is now the optimal solution:
what is linear cost behaviour? - ANS-variable costs
y=mx
what is variable costs? - ANS-cost per unit multiplied by the number of units
What do we need to think about before we use a cost per unit? - ANS-must look at capacity (do
you have capacity to make more units), what is the relevant range in which we are operating (is
the range of production where variable cost per unit is true)
What are the non-linear cost behaviours? - ANS-fixed cost y=b and mixed cost y=mx +b
what are some examples of fixed cost? - ANS-raw materials, labour, salary potentially, rent or
lease costs
