Question

Below is a Linear Programming problem scenario and algebraic formulation. Review the scenario and identify what if any errors there are in the algebraic formulation. Select all that apply. Sage Lorimer runs a small chain of jewelry boutiques. She has hired a Marketing Inten to help choose the number and types of advertising that should be used to promote the stores. The table below shows the types of advertising available over the next month and the unit cost. Sage wants to ensure the largest number of people see the ads. The total advertising budget is S75,000. Exposure (people/Ad) 8,000 10,000 15,000 30,000 Cost (S/Ad) $1,000 $3,000 $4,000 $8,000 Advertisement Type Ad Bookings Available unlimited 15 ads 10 ads 5 ads Online Media Ad Newspaper Ad Radio Ad Television Ad Algebraic LP Problem Formulation: Let x,-the # of Ads of Type / to buy with i-(1 for Online Media, 2 for Newspaper Ads: 3 for Radio Ads, and 4 for Television Ads) Subject To 1,000x, +3,000x2+ 4,000x3 + 8,000X4 75000 Ad Budget Constraint

Answer 1

a. Maximize vs Minimize not stated- The objective function has to be necessarily maximized or minimized.

c. Missing Non-negativity constraints- All 4 variables ie X1, X2, X3and X4 have to be non-negative and the same should be mentioned in the formulation.

e. Objective function has the wrong units of measure- Unit of the objective function is the number of people exposed( (People/Ad) x Number of Ads). However, in the formulation, $ is mentioned in the objective function which is incorrect.

g. Integer constraints not needed- Since X1, X2, X3 and X4 are number of ads, they would be integers only, hence mentioning integer constraints is not necessarily required.

i. In the constraint, X1 + X2 + X3 + X4 >= 0, the label is missing. It is required to mention the type of constraint for each constraint.