Question

Please assist with the following problems:

Q1. For each of the following decision-making problems, determine whether the problem involves constrained or unconstrained optimization; what the objective function is and, for each constrained problem, what the constraint is; and what the choice variables are.

a. We are ordering a new commercial aircraft from Boeing and we choose how to allocate seats between the first-class section and the coach section of the aircraft. The new aircraft has a total of 1800 square feet of seating space. First-class seats require 10 square feet of space per seat and coach class seats require 6 square feet of space per seat. We expect to earn 1.75 times as much revenue per seat in first-class as in coach seating, and we will cancel any flight that is not completely booked (i.e. all seats are sold). (1.5 pts)

b. We develop pharmaceutical drugs to treat inflammation diseases and drugs to treat infectious diseases. Our research and development budget must be split between these two separate divisions of drug research. Your job is to determine whether we are allocating our limited R&D spending between the two divisions in the best possible way. (1.5 pts)

c. We aren’t earning enough profits. Your job is to redesign our global market structure to make sure that we maintain the optimal presence in every profitable market on the planet! Get to work now. (1.5 pts)

Q2. A decision maker is choosing the levels of two activities, X and Y, so as to maximize total benefits under a given budget. The prices and marginal benefits of the last units of X and Y are denoted PX, PY, MBX, and MBY.

a. If PX = $30, PY = $40, MBX = 420, and MBY = 640, what should the decision maker do? (1.5 pts)

b. If PX = $15, PY = $17.50, MBX = 750, and MBY = 840, what should the decision maker do? (1.5 pts)

c. If PX = $56, PY = $14, MBX = 2,800, and MBY = 1,050, how many units of Y can be obtained if X is reduced by one unit? How much will benefits increase if this exchange is made? (1.5 pts)

d. If the substitution in part c continues until the point of equilibrium is reached, and MBX rises to 3,360, then what will MBY be in equilibrium? (1.5 pts)

Q3. You are interviewing three people for one sales job. On the basis of your experience and insight, you believe Jack can sell 64 widgets per day, Jill can sell 50 widgets per day, and John can sell 100 widgets per day. The daily salary each person is asking is as follows: Jack, $100; Jill, $100; and John, $300. How would you rank the three applicants? (3 x 1.5 pts)

Answer 1

Solution(s):

a)

Constrained or Unconstrained : Constrained

Objective Function Identifying what PC's are affordable and suit the taste of the staff

If Constrained

Constraint The budget , tastes ,number of staff members

Choice Available : List down common features acceptable by staff

Remove that fall above budget given the number of staff members

b)

Constrained or Unconstrained :Constrained

Objective FunctionREdesigning the advertising programme(for TV,direct mail and magazine) with new strategies to generate profits

If Constrained:

Constraint: TV, direct-mail, and magazine

Choice Available:

Reviewing earlier programme and assessing mistakes.

Redesigning with respect to consumer preferences as to what effects their decisions the most.

Allocating the methods accordingly.

c)

Constrained or Unconstrained :Constrained

Objective Function: Reallocating machinery,the numbre of workes and raw materials needed to meet quota without overspending

If Constrained:

Constraint: Amount spent

Choice Available

Assuring efficient use and allocation of optimum number of workers and raw material such that production is maximized.