MHT CET · Maths · Linear Programming
A production unit makes special type of metal chips by combining copper and brass. The standard weight of the chip must be at least 5 gms. The basic ingredients i.e. copper and brass cost ₹8 and ₹5 per gm. The durability considerations dictate that the metal chip must no contain more than 4 gms of brass and should contain minimum 2 gms of copper. Then the minimum cost of the metal chip satisfying the above conditions is
- A ₹ 36
- B ₹ 31
- C ₹ 30
- D ₹ 40
Answer & Solution
Correct Answer
(B) ₹ 31
Step-by-step Solution
Detailed explanation
Let \(x\) and \(y\) denote the quantity of the basic ingredients of copper and brass respectively.
\(\therefore \quad\) cost, \(z=8 x+5 y\)
Constraints are,
\(\begin{aligned}
& x+y \geq 5 \\
& x \geq 2 \\
& y \leq 4 \\
& x \geq 0, y \geq 0
\end{aligned}\)
\(\therefore \quad\) Feasible region is as shown in the figure.
\(\therefore \quad\) Corner points of the feasible region are \(\dot{A}(2,4), B(2,3)\) and \(C(5,0)\)
\(\therefore \quad \mathrm{z}\) at \(\mathrm{A}=36\),
z at \(\mathrm{B}=31\),
z at \(\mathrm{C}=40\)
\(\therefore \quad\) Minimum cost is ₹ 31 .
\(\therefore \quad\) cost, \(z=8 x+5 y\)
Constraints are,
\(\begin{aligned}
& x+y \geq 5 \\
& x \geq 2 \\
& y \leq 4 \\
& x \geq 0, y \geq 0
\end{aligned}\)
\(\therefore \quad\) Feasible region is as shown in the figure.
\(\therefore \quad\) Corner points of the feasible region are \(\dot{A}(2,4), B(2,3)\) and \(C(5,0)\)
\(\therefore \quad \mathrm{z}\) at \(\mathrm{A}=36\),
z at \(\mathrm{B}=31\),
z at \(\mathrm{C}=40\)
\(\therefore \quad\) Minimum cost is ₹ 31 .
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\int_{0}^{\pi / 2} \frac{\sin x-\cos x}{1-\sin x \cdot \cos x} d x\) is equal toMHT CET 2009 Easy
- A line makes an angle of \(45^{\circ}\) with \(x\) -axis and congruent angles with \(y\) and \(z\) -axes, then the direction cosines of the line areMHT CET 2020 Easy
- The probability distribution of a discrete r. v. \(X\) is
then value of \(\mathrm{P}(\mathrm{X} \leq 2)\) isMHT CET 2020 Medium - If \(\alpha+\beta+\gamma=\pi\), then the expression \(\sin ^2 \alpha+\sin ^2 \beta-\sin ^2 \gamma\) has the valueMHT CET 2024 Easy
- The particular solution of the differential equation \(\left(1+e^{2 x}\right) d y+e^x\left(1+y^2\right) d x=0\) at \(x=0\) and \(y=1\) isMHT CET 2021 Medium
- If \(\mathrm{x}=\mathrm{a}\left(\mathrm{t}-\frac{1}{\mathrm{t}}\right)\) and \(\mathrm{y}=\mathrm{b}\left(\mathrm{t}+\frac{1}{\mathrm{t}}\right)\), then \(\frac{\mathrm{dy}}{\mathrm{dx}}=\)MHT CET 2021 Medium
More PYQs from MHT CET
- Which of the following on reaction with Grignards reagent followed by hydrolysis forms tertiary alcohol?MHT CET 2025 Medium
- An insulated container contains a monoatomic gas of molar mass ' \(m\) '. The container is moving with velocity ' \(V\) '. If it is stopped suddenly, the change in temperature is ( \(\mathrm{R}=\) gas constant)MHT CET 2024 Medium
- The vector equation of the lien whose Cartesian equations are \(y\) \(=2\) and \(4 x-3 z+5=0\) isMHT CET 2021 Medium
- A liquid kept in a cylindrical vessel is rotated about vertical axis through the centre
of circular base. The difference in the heights of the liquid at the centre of vessel and
its edge is \((\mathrm{R}=\) radius of vessel, \(\omega=\) angular velocity of rotation, \(\mathrm{g}=\) acceleration
due to gravity)MHT CET 2020 Hard - What is the value of \(\angle \mathrm{S}\)-S-S in puckered \(\mathrm{S}_8\) rhombic sulfur?MHT CET 2023 Easy
- Identify ' \(A\) ' in the following reaction.
\(\underset{\text { (excess) }}{\mathrm{A}}\) + \(\underset{\text { (excess) }}{\mathrm{Acetyl \ chloride}}\) \(\xrightarrow[\mathrm{AlCl}_3]{\text { Anhydrous }} 1\)-Chloroacetophenone + 4-chloroacetophenoneMHT CET 2025 Medium