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Write down the initial simplex table for the following problem. Find the first pivot column and...

Write down the initial simplex table for the following problem. Find the first pivot column and the first pivot. Do not complete the simplex algorithm.

A department store has up to 16000TL to spend on television advertising for sale. All ads will be placed with one television station. A 30-second ad costs 1000TL on daytime TV and is viewed by 14000 potential customers, 1800TL on prime-time TV and is viewed by 18000 potential customers, and 1500TL on late-night TV and is viewed by 14400 potential customers. The television station will not accept a total of more than 15 ads in all three time periods. How many ads should be placed in each time period in order to maximize the number of potential customers who will see the ads? How many potential customers will see the ads?

Solutions

Expert Solution

Let x, y and z be the number of ads on day time prime time and late night TV respectively. The equaltions will be:

Maximize Z: 14000x + 18000y + 14400z

subject to,

1000x + 1800y + 1500z = <=16,000

x+y+z <=15

x,y,z>0

Introducing slack variables, we get,

Maximize Z: 14000x + 18000y + 14400z + 0S1 + 0S2

subject to,

1000x + 1800y + 1500z + S1 =16,000

x+y+z + S2 =15

The simplex table will look like:

Explanation of the calculation is:

The element highlighted in orange is key element.

For the next pivot, values in key row = Old Number/Key Element

Values in other row = Old Number - (Number in Corresponding Row*Number in Corresponding Column)/Key element

Pivot will be calculated as:

ekkarill92 answered 1 year ago
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