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Linear Programm...

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  • Question 1
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    The Convex Polygon Theorem states that the optimum (maximum or minimum) solution of a LPP  is attained at atleast one of the ______ of the convex set over which the solution is feasible.

  • Question 2
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    Directions For Questions

    A company manufactures two types of calculators - normal calculator and scientific calculator. Due to demand in the market, the company must produce a minimum of $$100$$ normal and $$80$$ scientific calculators daily. The constraints on the manufacturing limits the production to a maximum of $$200$$ normal and $$170$$ scientific calculators. Also, a minimum of total $$200$$ calculators must be produced in a day. A normal calculator sold incurs a loss of Rs. $$2$$, whereas a scientific calculator gains a profit of Rs. $$5$$.

    $$($$Take $$x$$ and $$y$$ as the quantity of normal and scientific calculators produced in a day respectively.$$)$$

    ...view full instructions

    In order to obtain maximum profit, the quantity of normal and scientific calculators to be manufactured daily is:

  • Question 3
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    The region on the graph sheet with satisfies the constraints including the non- negativity restrictions is called the _______ space.

  • Question 4
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    Directions For Questions

    A company manufactures two types of calculators - normal calculator and scientific calculator. Due to demand in the market, the company must produce a minimum of $$100$$ normal and $$80$$ scientific calculators daily. The constraints on the manufacturing limits the production to a maximum of $$200$$ normal and $$170$$ scientific calculators. Also, a minimum of total $$200$$ calculators must be produced in a day. A normal calculator sold incurs a loss of Rs. $$2$$, whereas a scientific calculator gains a profit of Rs. $$5$$.

    $$($$Take $$x$$ and $$y$$ as the quantity of normal and scientific calculators produced in a day respectively.$$)$$

    ...view full instructions

    In order to maximize the profit of the company, the optimal solution of which of the following equations is required?

  • Question 5
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    Directions For Questions

    A farmer has $$10$$ acres of land to plant wheat and rye. He has to plant atleast $$7$$ acres. Each acre of wheat costs $$\$200$$ and each acre of rye costs $$\$100$$ to plant. He has only $$\$1200$$ to spend. Moreover, the farmer has to get the planting done in $$12$$ hours and it takes $$1$$ hour to plant an acre of wheat and $$2$$ hours to plant an acre of rye. An acre of wheat yields a profit of $$\$500$$ and an acre of rye yields a profit of $$\$300$$.

    $$($$Take $$x$$ and $$y$$ as the acres of wheat and rye planted respectively$$)$$

    ...view full instructions

    How many acres of each (wheat and rye) should the farmer plant in order to get maximum profit?

  • Question 6
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    Directions For Questions

    A farmer has $$10$$ acres of land to plant wheat and rye. He has to plant atleast $$7$$ acres. Each acre of wheat costs $$\$200$$ and each acre of rye costs $$\$100$$ to plant. He has only $$\$1200$$ to spend. Moreover, the farmer has to get the planting done in $$12$$ hours and it takes $$1$$ hour to plant an acre of wheat and $$2$$ hours to plant an acre of rye. An acre of wheat yields a profit of $$\$500$$ and an acre of rye yields a profit of $$\$300$$.

    $$($$Take $$x$$ and $$y$$ as the acres of wheat and rye planted respectively$$)$$

    ...view full instructions

    How many acres of land will be left unplanted if the farmer aims for a maximum profit?

  • Question 7
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    If $$a,b,c \in +R$$ such that $$\lambda abc$$ is the minimum value of $$a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2)$$, then $$\lambda=$$

  • Question 8
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    Consider the objective function $$Z = 40x + 50y$$ The minimum number of constraints that are required to maximize $$Z$$ are

  • Question 9
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    Maximum value of $$z=3x+4y$$ subject to $$x-y\le -1,-x+y\le 0,x,y\ge 0$$ is given by?

  • Question 10
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    The objective function $$z={ x }_{ 1 }+{ x }_{ 2 }$$, subject to $${ x }_{ 1 }+{ x }_{ 2 }\le 10,{ -2x }_{ 1 }+3{ x }_{ 2 }\le 15,{ x }_{ 1 }\le 6$$, $${ x }_{ 1 },{ x }_{ 2 }\ge 0$$ has maximum value .................. of the feasible region.

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