help please thx

paint fair company advertises its weekly sales in newspapers, television, and radio. Each hundred dollars spent in advertising in newspapers is estimated to reach an exposure of 14 buying customers, and each hundred dollars in tv reaches an exposure 17 buying customers and each hundred dollars in radio reaches an exposure of 12 buying custumers.The company has an agreement with all three media services that it will spend less than 25% of its total money in each medium.further that it is agreed that the combined newspaper and television budget will not be larger than three times the radio budget. The company has just decided to spend no more than 700,000dollares on advertising. How much should the comapny budget for each medium if it is interested in reaching as many buying custumers as possible?

i just need the lp model so i can solve the rest...can you please help me with this...thank you very much god bless you

please help, just for today..i really need it.thank you

If you put

Xn=newspaper
Xr=radio
Xt=TV
then the objective function is
Z=0.14Xn+0.12Xr+0.17Xt
B=700000 = budget
The budget constraints are therefore
Xn<0.25B
Xr<0.25B
Xt<0.25B
The competition constraint is
Xn+Xt<3Xr
So proceed with the algorithm you have learned to solve for the optimal solution. If you need additional information, here is a good reference:
http://en.wikipedia.org/wiki/Simplex_algorithm

Sure! To solve this problem using linear programming, let's define the decision variables and the objective function:

Decision Variables:
Let N be the amount spent on newspaper advertising (in hundreds of dollars).
Let T be the amount spent on television advertising (in hundreds of dollars).
Let R be the amount spent on radio advertising (in hundreds of dollars).

Objective Function:
Maximize the total number of buying customers reached.

Now, let's define the constraints based on the given information:

1. Maximum budget constraint:
N + T + R ≤ 7000 (since the total budget is $700,000).

2. Newspaper exposure constraint:
N/100 * 14 ≥ 0 (since each hundred dollars in newspaper advertising reaches 14 buying customers).

3. Television exposure constraint:
T/100 * 17 ≥ 0 (since each hundred dollars in television advertising reaches 17 buying customers).

4. Radio exposure constraint:
R/100 * 12 ≥ 0 (since each hundred dollars in radio advertising reaches 12 buying customers).

5. Media service agreement constraint:
N ≤ 0.25 * (N + T + R) (spending on newspaper advertising should be less than 25% of the total budget).
T ≤ 0.25 * (N + T + R) (spending on television advertising should be less than 25% of the total budget).
R ≤ 0.25 * (N + T + R) (spending on radio advertising should be less than 25% of the total budget).

6. Combined newspaper and television budget constraint:
N + T ≤ 3R (the combined newspaper and television budget should not be larger than three times the radio budget).

Now, you can solve this linear programming problem to find the optimal values for N, T, and R, which will tell you how much the company should budget for each medium.

Sure! I can help you create a linear programming (LP) model for this problem. Let's start by defining some variables:

N = amount spent on advertising in newspapers (in hundreds of dollars)
T = amount spent on advertising on television (in hundreds of dollars)
R = amount spent on advertising on radio (in hundreds of dollars)

Now, let's define the objective function. The objective is to maximize the total exposure to buying customers. Each medium has a different exposure rate per hundred dollars spent, so we can write the objective function as:

Maximize: 14N + 17T + 12R

Next, we need to consider the constraints. The total budget should not exceed $700,000, so we have the constraint:

N + T + R ≤ 7000

Additionally, the company has a restriction that each medium should not account for more than 25% of the total budget. We can represent this constraint as:

N ≤ 0.25 * (N + T + R)
T ≤ 0.25 * (N + T + R)
R ≤ 0.25 * (N + T + R)

Lastly, the combined newspaper and television budget should not be larger than three times the radio budget:

N + T ≤ 3R

Now we have our LP model. To summarize:

Maximize: 14N + 17T + 12R
Subject to:
N + T + R ≤ 7000
N ≤ 0.25 * (N + T + R)
T ≤ 0.25 * (N + T + R)
R ≤ 0.25 * (N + T + R)
N + T ≤ 3R

You can now use any LP solver or optimization software to solve this model and find the optimal budget allocations for each medium (N, T, R).