52:620:321 Management Science – I. Instructor: Dr. Neha Mittal Email: firstname.lastname@example.org Website: www.crab.rutgers.edu/~nmittal. Management Science - I. Book Introduction to Management Science – Anderson, Sweeney and Williams, 12 th edition Exams and Assignments Grading
Instructor: Dr. Neha Mittal
Is the body of knowledge involving quantitative approaches to decision making. It is also referred as
Frederic W. Taylor of the early 1900’s provided the foundation for use of quantitative methods. MS research originated during the World War II times and flourished later on with the aid of computers.
Define the problem.
Identify the set of alternative solutions.
Determine the criteria for evaluating alternatives.
Evaluate the alternatives.
Choose an alternative (make a decision).
Implement the chosen alternative.
Evaluate the results.What is Decision Making
Structuring the Problem
Analyzing the Problem
Structure the problem
Analyze the problem
Implement the solution
Evaluate the results
Objective Function – a mathematical expression that describes the problem’s objective, such as maximizing profit or minimizing cost
Constraints – a set of restrictions or limitations, such as production capacities
Uncontrollable Inputs/Parameters – factors that are not under the control of the decision maker
Decision Variables – an unknown quantity representing a decision that needs to be made. It is the quantity the model needs to determine.
The analyst attempts to identify the alternative (the set of decision variable values) that provides the “best” output for the model.
The “best” output is the optimal solution.
If the alternative does not satisfy all of the model constraints, it is rejected as being infeasible, regardless of the objective function value.
If the alternative satisfies all of the model constraints, it is feasible and a candidate for the “best” solution.
Iron Works, Inc. manufactures two
products made from steel and just received
this month's allocation of b pounds of steel.
It takes a1 pounds of steel to make a unit of product 1
and a2 pounds of steel to make a unit of product 2.
Let x1 and x2 denote this month's production level of
product 1 and product 2, respectively. Denote by p1 and
p2 the unit profits for products 1 and 2, respectively.
Iron Works has a contract calling for at least m units of
product 1 this month. The firm's facilities are such that at
most u units of product 2 may be produced monthly.
Develop a mathematical model which maximizes profit.
s.t. a1x1 + a2x2<b
x1 , x2> 0
s.t. 2x1 + 3x2< 2000
Suppose b = 2000, a1 = 2, a2 = 3, m = 60, u = 720, p1 = 100,
p2 = 200. Rewrite the model with these specific values for the uncontrollable inputs.
The optimal solution to the current model is x1 = 60 and x2 = 626 2/3.
A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day.
Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily.
To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day.
If each scientific calculator sold results in a $2 profit, and each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits?Problem
Ponderosa Development Corporation
(PDC) is a small real estate developer that builds
only one style house. The selling price of the house is
Land for each house costs $55,000 and lumber,
supplies, and other materials run another $28,000 per
house. Total labor costs are approximately $20,000 per house.
Ponderosa leases office space for $2,000 per month. The cost of supplies, utilities, and leased equipment runs another $3,000 per month.
The one salesperson of PDC is paid a commission of $2,000 on the sale of each house. PDC has seven permanent office employees whose monthly salaries are given on the next slide.
VP, Development 6,000
VP, Marketing 4,500
Project Manager 5,500
Office Manager 3,000
Identify all costs and denote the marginal cost and marginal revenue for each house.
salaries, leases, utilities
Marginal / variable costs
commission, land, materials, labor
selling price of each house
Write the monthly cost function c (x), revenue function r (x), and profit function p (x).
c (x) = variable cost + fixed cost = 105,000x + 40,000
r (x) = 115,000x
p (x) = r (x) - c (x) = 10,000x - 40,000
What is the breakeven point for monthly sales
of the houses?
r (x ) = c (x )
x = 4
What is the monthly profit if 12 houses per month are built and sold?
p (x) = r (x) – c (x)
p (12) = $80,000
Total Revenue =
Thousands of Dollars
Total Cost =
40,000 + 105,000x
Break-Even Point = 4 Houses
Number of Houses Sold (x)
As part of a loan application to buy Lakeside Farm, (a property Joe hopes to develop as a bed-and-breakfast operation), the prospective owners have projected:
Monthly fixed cost (loan payment, taxes, insurance, maintenance) $6000
Variable cost per occupied room per night $ 20
Revenue per occupied room per night $ 75
Write the expression for total cost per month. Assume 30 days per month.
Write the expression for total revenue per month.
If there are 12 guest rooms available, can they break even?Assignment: Breakeven Analysis