Question A paper mill produces paper rolls in two standard widths; one with width 20 in. and the other with width 50 in. It is desired to produce new rolls with different widths as indicated below. The new rolls are to be produced by cutting the rolls of standard widths to minimize the trim loss. Formulate the problem as an LP problem.  

DISCRETE OF STRUCTURES Task Performance: Matrix Operations Upload a photo of your answer sheet showing your name and solution. (4 items x 10 points) 1) What is 2A + 5B if Matrix A = 1 2 -31 -5 4 2 2] and Matrix B -2 6 41 -1 -2 31 2) What is 3A - 2B if -3 1 4 -31 Matrix A = -2 4 and Matrix B = -2 5 -11 -2 4 E 3) What is BA if 3 Matrix A = 0 -2 5 12-1 0 -1 6 and Matrix B = 3 -5 2 2 11 4 -21 -1) 4) What is 3AT-2BT if Matrix A = XA = 1 -3) and Matrix B [6 -2]

 Southside Systems has $60 million of outstanding debt with a 7% required rate of return. Southside has a required return on assets of 13%, an EBIT of $45 million, and corporate tax rate of 21%. a. Calculate Southside’s present value of the interest tax shields and total firm value. b. Calculate Southside’s gain from leverage if there are personal taxes of 20% on stock income and 30% on debt income.

roblem 6 A reinforced concrete footing supports a \( 450 \mathrm{~mm} \) square column. GIVEN : Thickness of the footing \( =645 \mathrm{~mm} \) Effective depth of the flexural reinforcement \( =545 \mathrm{~mm} \) Column axial loads: \( \mathrm{DL}=800 \mathrm{KN} \) \( \mathrm{LL}=800 \mathrm{KN} \) \( \mathrm{U}=1.2 \mathrm{DL}+1.6 \mathrm{LL} \) roblem 6 A reinforced concrete footing supports a \( 450 \mathrm{~mm} \) square column. GIVEN : Thickness of the footing \( =645 \mathrm{~mm} \) Effective depth of the flexural reinforcement \( =545 \mathrm{~mm} \) Column axial loads: \( \mathrm{DL}=800 \mathrm{KN} \) \( \mathrm{LL}=800 \mathrm{KN} \) \( \mathrm{U}=1.2 \mathrm{DL}+1.6 \mathrm{LL} \) Materials : Concrete, \( \mathrm{f}_{\mathrm{c}}{ }^{\prime}=24 \mathrm{MPa} \) Steel, \( \mathrm{f}_{\mathrm{y}}=280 \mathrm{MPa} \) Allowable effective soil bearing capacity \( =219.38 \mathrm{kPa} \) Strength reduction factors: \( \quad 0.75 \) for shear \( 0.90 \) for bending 1. Determine the length required for the footing \( (\mathrm{m}) \) if site conditions limits the width of the footing to \( 2.0 \mathrm{~m} \). A. \( 3.65 \) B. \( 2.45 \) C. \( 4.25 \) D. \( 5.20 \) 2. Determine the no. of pcs \( 28 \mathrm{~mm} \phi \) flexural reinforcements along the long dimension of the footing. A. 8 B. 10 C. 12 D. 14 3. Determine the no. of pcs \( 28 \mathrm{~mm} \phi \) reinforcements along the short dimension of the footing over a bandwidth (centered on centerline of the column), the bandwidth having a width equal to the length of the short side of the footing. A. 6 B. 9 C. 11 D. 13 4. Determine the no. of pcs \( 28 \mathrm{~mm} \phi \) reinforcements (per side) along the short dimension of the footing outside the center bandwidth of the footing. A. 2 B. 3 C. 4 D. 5

simplify the answer 12.5-4. Concentration of NaOH Solution in a Triple-Effect Evaporator. A forced-circulation triple-effect evaporator using forward feed is to be used to concentrate a 10 wt% NaOH solution entering at 37.8°C to 50%. The steam used enters at 58.6 kPa gage. The absolute pressure in the vapor space of the third effect is 6.76 kPa. The feed rate is 13 608 kg/h. The heat-transfer coefficients are U1 = 6246, U2 = 3407, and U3 = 2271 W/m2.K. All effects have the same area. Calculate the surface area and steam consumption. Ans. A = 97.3 m². S=5284 kg steam/h 410

Coursework 3.3 Write the state-space representation for the following systems: Yilt 7. 421t) К. M2 KI m W fit) bi yait) be -Ma RA 2. 20 + yilt) Ta í It) = Uzlt) Milt=VLE R2 R2

Help please A thin walled cylindrical pressure vessel is subjected to an internal pressure which varies from 750 KPa to 3550 KPa continuously. The diameter of the shell is 1.5 m. Find the required thickness of the cylinder wall based on yield point of 480 MPa, net endurance limit of 205 MPa and a factor of safety of 2.5. A camshaft 19 mm. in diameter is mounted on ball bearings and carries a cam midway from the bearings. The follower, which weighs 2.8 KN, is out of adjustment so that impact is produced when it is contacted by the cam. The height h of fall equals 0.254 mm. The shaft is made of AISI C1045 steel. Determine the maximum bending stress in the shaft.