Two women have decided to start a cottage industry that will be run out of their...

 

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Two women have decided to start a cottage industry that will be run out of their homes. They are going to make two types of specialty shirts, handmade beaded shirts and embroidery shirts. The total gross profit is given by p(x, y) = -2x² + 60x-3y² + 72y + 100. The constraint on their profit is a total of 20 shirts. Using this information, answer the following questions: a) Create the Lagrangian equation (2 marks) b) Find the three first order conditions (Lx, Ly, La) (3 marks) c) Solve for the optimal levels of x and y (5 marks) d) Give the economic interpretation of the multiplier 2 in the context of this question (2 marks) e) By how much would profit change if the constraint is increased to 25 shirts. (3 marks) Two women have decided to start a cottage industry that will be run out of their homes. They are going to make two types of specialty shirts, handmade beaded shirts and embroidery shirts. The total gross profit is given by p(x, y) = -2x² + 60x-3y² + 72y + 100. The constraint on their profit is a total of 20 shirts. Using this information, answer the following questions: a) Create the Lagrangian equation (2 marks) b) Find the three first order conditions (Lx, Ly, La) (3 marks) c) Solve for the optimal levels of x and y (5 marks) d) Give the economic interpretation of the multiplier 2 in the context of this question (2 marks) e) By how much would profit change if the constraint is increased to 25 shirts. (3 marks)

Answer rating: 100% (QA)

a Create the Lagrangian equation 2 marks ANSWER L 2x60x3y72y 100 20xy Where x number of beaded shirts y number of embroidery shirts Lagrange multiplie... View the full answer