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1.Suppose a consumer consuming two commodities X and Y has the following utility function TU= X0.5 Y0.5. If price of good X and Y are 2 and 3 respectively and income constraint is Birr 60.
A. Formulate the budget equation
B. Find the MRSXY at optimum.
C. Find the quantities of good X and Y which will maximize utility
Write a rule for a function, P
P, that gives the perimeter of a square in inches when the side length is x
x inches.
A plate 100 mm wide, 200 mm long, and 12 mm thick is loaded in tension in the direction of the length. The plate contains an edge crack with the crack length of 16 mm. The material is steel with KIC = 80 MPa√m, and Sy = 950 MPa. Determine the maximum possibleload that can be applied before the plate (a) yields, and (b) has uncontrollable crack growth.
A thick-walled cylinder of 450 mm outside diameter and 340 mm inside diameter, made of BS 535 A99 steel alloy, is subjected to an internal pressure of P. The maximum depth of radial crack in longitudinal direction on the outer surface of this cylinder is 22 mm. If the factor of safety against fracture failure of this cylinder is 3.1, what maximum safe internal pressure (P) can be applied to the cylinder?
The plate with a circular hole in the following figure is subjected to a tensile stress of σ0 at the boundaries AB and CD. The plate is made of steel 4340 material with Sy = 1515 MPa, if b = 200 mm, a = 50 mm, and the plate thickness, t = 20 mm, determine the maximum value of σ0 that can be safety applied considering a safety factor of 1.5.
Perform another analysis to calculate the maximum value of σ0 assuming two edge cracks of 2 mm each at points E and F of the hole, in directions perpendicular to the loading direction. What is the percentage of reduction of the allowable stress (σ0) if cracks are present?
A cylinder contains pressurized gas at 500 MPa and has the outer and inner diameters of 600 mm and 450 mm respectively. Determine the maximum permissible radial crack dimension on the outer surface of the cylinder in order to avoid further propagation of crack based on safety factor of 2.0. The cylinder material is BS 816 M40 of yield strength 1515 MPa.
q1
ABC has the following capital structure. What is the WACC for the company?
Debt:
Bond 1. 400,000 bonds with a coupon rate of 6% (paid semi-annually), a price quote of 110.0 and have 20 years to maturity.
Bond 2. 300,000 zero coupon bonds (semi-annual compounding) with a price quote of 40.0 and 25 years until maturity.
Preferred stock:
600,000 shares of 4 percent preferred stock with a current price of $60, and a par value of $100.
Common stock:
12,000,000 shares of common stock, with a price of $80, and a beta of 1.3.
Market:
The corporate tax rate is 40 percent, the market risk premium is 9%, and the risk-free rate is 4%.
Question 2
The ABC stock has a beta of 1.4. The company just paid a dividend of $2.0, and the dividend is expected to grow at 6% per year, indefinitely. The expected market return is 14%, and the risk-free is 4%. The most recent stock price for ABC is $60. Calculate the cost of equity using the SML method.
A rectangular plate of length 2h = 20 mm, width 2b = 50 mm and thickness 5 mm, containing a central crack of length 2a, is subjected to a uniform tensile stress of 40 MPa in the direction of its length as shown in the figure. Determine the maximum permissible crack dimension to avoid its further propagation choosing a factor of safety of 1.6. The plate material is BS 816M40.
Cylinder subjected to internal pressure with an internal diameter of 350 mm and a 25 mm wall thickness. For the cylinder material, KIC = 80 MPa√m, Sy = 1172 MPa, and Sut = 1324 MPa. If the cylinder contains a radial crack in the longitudinal direction of depth 12.5, mm determine the pressure that will cause uncontrollable crack growth.
gwi nam is working on a fluid which flows at 10lb/min and operates at steady flow process in his laboratory.The fluid has an initial pressure of 200 psia dropped to 20 psia.Its speed increases from 200 ft/s to a final velocity of 1000ft/s.The internal energy decreases 25 BTU/lbm and the specific volumes increases from 18 cubic ft/lb.Assuming that no heat is transferred.Determine the work done in BTU/min.
