D2 June 2009 Q5
5. While solving a maximising linear programming problem, the following tableau was obtained.
| Basic Variable | \(x\) | \(y\) | \(z\) | \(r\) | \(s\) | \(t\) | value |
|---|---|---|---|---|---|---|---|
| \(z\) | \(\tfrac{1}{4}\) | \(-\tfrac{1}{4}\) | 1 | \(\tfrac{1}{4}\) | 0 | 0 | 2 |
| \(s\) | \(\tfrac{5}{4}\) | \(\tfrac{7}{4}\) | 0 | \(-\tfrac{3}{4}\) | 1 | 0 | 4 |
| \(t\) | 3 | \(\tfrac{5}{2}\) | 0 | \(-\tfrac{1}{2}\) | 0 | 1 | 2 |
| \(P\) | −2 | −4 | 0 | \(\tfrac{5}{4}\) | 0 | 0 | 10 |
(a) Write down the values of \(x\), \(y\) and \(z\) as indicated by this tableau. (2)
(b) Write down the profit equation from the tableau. (2)
| Scheme | Marks |
|---|---|
| \(x = 0,\ y = 0,\ z = 2\) | B2,1,0 |
| (2) |
Notes
1B1: Any 2 out of 3 values correct
2B1: All 3 values correct.
| Scheme | Marks |
|---|---|
| \(P - 2x - 4y + \dfrac{5}{4}r = 10\) | M1 A1 |
| (2) | |
| (4 marks) |
Notes
1M1: One equal sign, modulus of coefficients correct. All the right ingredients.
1A1: cao – condone terms of zero coefficient