Question
Solve the linear programming problem and determine the maximum profit to the manufacturer.
✓
Answer
We have Maximise Z = 100x + 170y Subject to
$3\text{x}+2\text{y}\leq3600,\text{x}+4\text{y}\leq1800,\text{x}\geq0,\text{y}\geq0$
From the shaded feasible region it is clear that the coordinates of corner points are (0, 0), (1200, 0), (1080, 180) and (0, 450).
On solving x + 4y = 1800 and 3x + 2y = 3600, we get x = 1080 and y = 180.
Hence, the maximum profit to the manufacture is 138600.
$3\text{x}+2\text{y}\leq3600,\text{x}+4\text{y}\leq1800,\text{x}\geq0,\text{y}\geq0$
From the shaded feasible region it is clear that the coordinates of corner points are (0, 0), (1200, 0), (1080, 180) and (0, 450).
On solving x + 4y = 1800 and 3x + 2y = 3600, we get x = 1080 and y = 180.
| Corner points | Corresponding value of Z = 100x + 170y |
| (0, 0) (1200, 0) (1080, 180) (0, 450) | 0 1200 ×100 = 12000 100 × 1080 + 170 × 180 = 138600 (maximum) 0 + 170 × 450 = 76500 |
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Using properties of determinants, solve the following for x:
→$ \begin{vmatrix} \text{x - 2} & \text{2x - 3 } & \text{3x - 4 } \\ \text{x - 4} & \text{2x - 9} & \text{2x - 16} \\ \text{x -8} & \text{2x - 27} & \text{3x -64} \end{vmatrix}=0$
Find the equation of the plane that bisects the line segment joining the points (1, 2, 3) and (3, 4, 5) and is at right angle to it.
Examine the differentiability of f, where f is defined by:
$\text{f(x)}=\begin{cases}\text{x[x]},&\text{if }0\leq\text{x}<2\$\text{x}-1)\text{x},&\text{if }2\leq\text{x}<3\end{cases}$
at x = 2.
→$\text{f(x)}=\begin{cases}\text{x[x]},&\text{if }0\leq\text{x}<2\$\text{x}-1)\text{x},&\text{if }2\leq\text{x}<3\end{cases}$
at x = 2.
Find the area of the region bounded by the parabola y2 = 2x + 1 and the line x - y - 1 = 0.
Prove that
$\text{L.H.S}=\sin\Big\{\tan^{-1}\frac{1-\text{x}^2}{2\text{x}}+\cos^{-1}\frac{1-\text{x}^2}{1+\text{x}^2}\Big\}=1$
→$\text{L.H.S}=\sin\Big\{\tan^{-1}\frac{1-\text{x}^2}{2\text{x}}+\cos^{-1}\frac{1-\text{x}^2}{1+\text{x}^2}\Big\}=1$
The relation S defined on the set R of all real number by the rule aSb iff a ≥ b is:
- An equivalence relation.
- Reflexive, transitive but not symmetric.
- Symmetric, transitive but not reflexive.
- Neither transitive nor reflexive but symmetric.
Find the equation of the plane through the line of intersection of the planes $\vec{\text{r}}\cdot(\hat{\text{i}}+3\hat{\text{j}})+6=0$ and $\vec{\text{r}}\cdot(3\hat{\text{i}}-\hat{\text{j}}-4\hat{\text{k}})=0,$ which is at a unit distance from the origin.
→Discuss the continuity and differentiability of the function $\text{f (x) = |x| + x - 1|}$ in the interval (-1, 2).
→Let C be a curve defined parametrically as $\text{x}=\text{a}\cos^3\theta,\text{y}=\text{a}\sin^3\theta,0\leq\theta\leq\frac{\pi}{2}.$ Determine a point P on C, where the tangent to C is parallel to the chord joining the points (a, 0) and (0, a).
→Find the point on the parabolas x2 = 2y which is closest to the point (0,5).