4. Zack consumes mangosteen(m) and chalta (c) and his satisfaction function from consuming these fruits is given by S = (m+2)(y+1) The price of mangosteen Pm = 4 and the price of chalta, Pc = 6. He has 130 taka to spend on these fruits. a. Write the Lagrangian function. b. Find the optimal levels of purchase for mangosteen and chalta. c. Use bordered Hessian to prove that the second order condition is satisfied. d. What is the value of the Lagrangian multiplier? Show that if the budget is increased by one Taka, the increase in his satisfaction level is equal to the value of the Lagrangian multiplier.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
4. Zack consumes mangosteen(m) and chalta (c) and his satisfaction function from consuming
these fruits is given by
S = (m+2)(y+1)
The price of mangosteen Pm = 4 and the price of chalta, Pc = 6. He has 130 taka to spend on these fruits.
a. Write the Lagrangian function.
b. Find the optimal levels of purchase for mangosteen and chalta.
c. Use bordered Hessian to prove that the second order condition is satisfied.
d. What is the value of the Lagrangian multiplier? Show that if the budget is increased by one Taka,
the increase in his satisfaction level is equal to the value of the Lagrangian multiplier.
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