The proplem: A local business Plans on advertizing their newproduct by purchasing advertisements on the radio and on TV. The business plansto purchase at least 60 total ads and they want to have at least twice as manyTV ads as radio ads. Radio ads cost $20 each and TV ads cost $80 each. Theadvertising budget is $4320. It is estimated that each radio ad will be heardby 2000 listeners and each TV ad will be seen by 1500 people. How many of eachtype of ad should be purchased tomaximize the number of people who will be reached by the advertisements?
Let X be the number of radio ads that are purchased and Y bethe number of TV ads.
1.Write down a linear inequality for the total number ofdesired ads.
2.Write down a linear inequality for the cost of the ads.
3.Recall that the business wants at least twice as many TVads as radio ads. Write down a linear inequality that expresses this fact.
4. There are two more constraints that must be met. theserelate to fact that there cannot be snegative numbers of advertisments. Write the two inequalities that model theseconstraints:
5.Next, write down the function for the number of peoplethat will be exposed to the advertisements. This is the Objective Function forthe problem. P=
You now have four linear inequalities and objectivefunction. These togather describe the situation. This combined set ofinequalities and objective function make up what is known mathmatically as a(linear programming) proplem. Write all of the inequalities and the objectivefunction together below. This is typically written as a list of constraints,with the objective function last.
6. to solve this proplem, you need to graph the(intersection) of all five inequalities on one common XY plane. Have the bottomleft be the origin, with the horizontal axis representing Y. Label the axeswith what they represent and label your lines as you graph them.
7. The shaded region in the above graph is called thefeasible region. Any (x,y) point in theregion corresponds to a possible number of the radio and TV ads that will meetall requirments of the proplem. However,the values that will maximize thenumber of people exposed to the ads will occur at one of the vertices orcorners of the region. Your region should have three corners, Find thecoordinate of these corners by solving the appropriate system of the linearequations. Be sure to show your work and label (x,y) coordinates of the cornersin your graph.
8.To find which number of radio and TV ads will maximize thenumber of people who are exposed to the business advertisements, evaluate theobjective function P for each of the vertices you found. Show your work
9. write a sentense describing how many of each type ofadvertisement should be purchased and what is the maximum number of people willbe exposed to the ad.
10. Reflective Writing
Did this project change the way you think about how math canbe applied to the real world?
Write one paragraph stating what ideas changedand why. If this project did not change the way you think, write how thisproject gave further evidence to support your exiting opinion about applyingmath. be specific
Let X be the number of radio ads that are purchased and Y bethe number of TV ads.
1.Write down a linear inequality for the total number ofdesired ads.
2.Write down a linear inequality for the cost of the ads.
3.Recall that the business wants at least twice as many TVads as radio ads. Write down a linear inequality that expresses this fact.
4. There are two more constraints that must be met. theserelate to fact that there cannot be snegative numbers of advertisments. Write the two inequalities that model theseconstraints:
5.Next, write down the function for the number of peoplethat will be exposed to the advertisements. This is the Objective Function forthe problem. P=
You now have four linear inequalities and objectivefunction. These togather describe the situation. This combined set ofinequalities and objective function make up what is known mathmatically as a(linear programming) proplem. Write all of the inequalities and the objectivefunction together below. This is typically written as a list of constraints,with the objective function last.
6. to solve this proplem, you need to graph the(intersection) of all five inequalities on one common XY plane. Have the bottomleft be the origin, with the horizontal axis representing Y. Label the axeswith what they represent and label your lines as you graph them.
7. The shaded region in the above graph is called thefeasible region. Any (x,y) point in theregion corresponds to a possible number of the radio and TV ads that will meetall requirments of the proplem. However,the values that will maximize thenumber of people exposed to the ads will occur at one of the vertices orcorners of the region. Your region should have three corners, Find thecoordinate of these corners by solving the appropriate system of the linearequations. Be sure to show your work and label (x,y) coordinates of the cornersin your graph.
8.To find which number of radio and TV ads will maximize thenumber of people who are exposed to the business advertisements, evaluate theobjective function P for each of the vertices you found. Show your work
9. write a sentense describing how many of each type ofadvertisement should be purchased and what is the maximum number of people willbe exposed to the ad.
10. Reflective Writing
Did this project change the way you think about how math canbe applied to the real world?
Write one paragraph stating what ideas changedand why. If this project did not change the way you think, write how thisproject gave further evidence to support your exiting opinion about applyingmath. be specific
