BUS107 Quantitative Methods

1. Linear Programming (LP) Model

2. Graphical LP Solution

3. LP Solution with Excel Solver (Computer Solution)

4. Sensitivity Analysis (Changes in the Constraint Right-Hand Side/Changes in the Objective Function Coefficient)

This question is about the application of linear programming (LP). Part (b) is a continuation of Part (a), and Part (c) is not related to Parts (a) and (b).

(a) DToys is planning a new social media and TV advertising campaign to reach people. A total budget of $30k is allocated to the campaign and the campaign must run on or within the budget. Moreover, to meet the development needs of the company, at least $10k must be allocated to each medium. It is estimated that every $1k spent on social media ad will reach 15 people and every $1k spent on TV ad will reach 10 people.

How should the budgeted amount be allocated between social media and TV? State verbally the objective, constraints and decision variables. Then formulate the problem as an LP model. After that, solve it using the graphical solution procedure. Please limit the answer to within two pages. (40 marks)

(b) Show that the worth per additional $1k of budget is reaching 15 more people, which is the same as the number of people reached per $1k spent on social media ad. Interpret what this result means in terms of allocating additional budget. Please limit the answer to within one page. (10 marks)

(c) Suppose your Residents' Committee (RC) invites you to give a speech introducing LP. The purpose of the speech is to attract senior citizens (over 65 years old, working in various industries before retirement, passionate about lifelong learning) to sign up for a basic LP course. The course teaches how to formulate a problem as an LP and how to solve it. Write down your complete speech, no more than 400 words. (50 marks)