Group Project
Part 1:
For the function
Solution:
To simulate the function f(x) in MATLAB following program is executed to plot and determine the tangent.
a)
The equation of tangent line is,
y = 1 – x, for x = 0,
y = x, for x = 1
Part 2:
Consider the following demand, supply and total cost functions:
Demand function:
Supply function:
Solution:
at equilibrium Demand function = Supply function.
Price is 9 units and quantity is 14 units.
We have to find the area under demand curve to get Consumer Surplus for this we need to integrate Demand curev w r t Quantity from q = 0 to Equilibrium
Quantity and then subtract area (Price)x(Quantity) at equilibrium
The consumer surplus is 881.
We have to find the area under demand curve to get Producer Surplus for this we need to integrate Supply curve w r t Quantity from q = 0 to Equilibrium
Quantity and then subtract it from area (Price)x(Quantity) at equilibrium
The Producer surplus is 881.
Part 3
If the function is subject to the constrain
Solution:
The critical point is -3 for the function.
The maximum is -6.0 and minimum is -8.0 of the function.
Part 4
Suppose that a restaurant has certain fixed costs per month of $5000. The fixed costs could be interpreted as rent, insurance etc. The marginal cost function of the restaurant is given by:
dc/dq = [0.8 (0.5q^{2} - 25q ) + 0.4]
wherec is the total cost in dollars of producing q units of good per week.
Solution:
The total cost of producing q_{1} is 1.7208 x 10^{11}, q_{2} is 6.8410 x 10^{11} and q_{3} is 1.7542 x 10^{11}
Total cost is increasing with the increase in the quantity. As it is observed from the graph of the function plotted between price and quantity.
Group |
Part 1 |
Part 2 |
Part 3 |
Part 4 |
2 |
f(x)= x^{2}-x+1 |
D: p=100 e^{-0.05}q S: p= 25 e^{0.05}q |
f(x,y)= 4x+3y g(x,y)=x^{2}+y^{2}=100 | dc/dq=[0.8(0.5q^2-25q)+0.4] s q_{1}=12000;q_{2}=19000;q_{3}=26000 |
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