a) Determine the objective function and formulate the system of inequalities satisfying the given constraints b) Sketch the feasible region satisfying the systems of those inequalities c) Sketch the objective function d) Find the number of packages of each grade of mixture that will realize maximum profit. State the profit

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Please provide me the full solutions for the question, a, b, c and d. This question is about linear programming. Thanks!
A nut seller mixes three kinds of nuts i.e. cashew, hazelnuts and pistachios.
The table below shows the mixture
Mixture
Grade A
Grade B
Weight of cashew
(gram)
20
10
Weight of hazelnut
(gram)
10
10
Weight of
pistachios (gram)
10
20
The nut seller has 10 kilogram of cashew, 7 kilogram of hazelnuts and 12 kilogram of
pistachios. The profit of each package of grade A and grade B mixture respectively are 30
cents and 40 cents. Let x be the number of packages for grade A mixture and y be the
number of packages for grade B mixture,
a) Determine the objective function and formulate the system of inequalities satisfying
the given constraints
b) Sketch the feasible region satisfying the systems of those inequalities
c) Sketch the objective function
d) Find the number of packages of each grade of mixture that will realize maximum
profit. State the profit
Transcribed Image Text:A nut seller mixes three kinds of nuts i.e. cashew, hazelnuts and pistachios. The table below shows the mixture Mixture Grade A Grade B Weight of cashew (gram) 20 10 Weight of hazelnut (gram) 10 10 Weight of pistachios (gram) 10 20 The nut seller has 10 kilogram of cashew, 7 kilogram of hazelnuts and 12 kilogram of pistachios. The profit of each package of grade A and grade B mixture respectively are 30 cents and 40 cents. Let x be the number of packages for grade A mixture and y be the number of packages for grade B mixture, a) Determine the objective function and formulate the system of inequalities satisfying the given constraints b) Sketch the feasible region satisfying the systems of those inequalities c) Sketch the objective function d) Find the number of packages of each grade of mixture that will realize maximum profit. State the profit
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