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business economics and finance

Questions and Answers of Business Economics And Finance

Maximize π = 4x1 + x2 subject to the same constraints in Problem 7.30. Maximize subject to =5x+10x2 2x13x248 4x112x2 168 8x16x2144 X1, X2 0
Use graphs to solve the following linear programming problems. Maximize subject to = 4x1 + 3x2 8x14x296 4x16x2120 18x13x2180 X1, X20
Maximize π = 5x1 + 4x2 subject to the same constraints in Problem 7.28 Maximize subject to = 4x1 + 3x2 8x14x296 4x16x2120 18x13x2180 X1, X20
Use graphs to solve the following linear programming problems. Maximize = 2x1 +3x2 subject to 2x12x2 32 3x19x2108 6x14x284 X1, X2 0
A landscaper wants to mix her own fertilizer containing a minimum of 50 units of phosphates, 240 units of nitrates, and 210 units of calcium. Brand 1 contains 1 unit of phosphates, 6 units of
A cereal manufacturer wants to make a new brand of cereal combining two natural grains x1 and x2.The new cereal must have a minimum of 128 units of carbohydrates, 168 units of protein, and 120 units
A maker of fine preserves earns $15 profit on its premium brand x1 and $6 profit on its standard brand x2. The premium-brand preserves take 7.5 minutes for peeling, 20 minutes for stewing, and 8
A bakery makes $4 profit on its wedding cakes x1 and $3 on its birthday cakes x2. Wedding cakes take 4 minutes for mixing, 90 minutes for baking, and 8 minutes for icing. Birthday cakes take 6
Find the total number of basic solutions that exist in Problem 7.22.Substituting v = 5 and n = 2 in the formula, N = = v! n!(vn)! 5! 5(4)(3)(2)(1) 2!(3)! 2(1)(3)(2)(1) 10
Use graphs to solve the following linear programming problems. Maximize subject to =5x+10x2 2x13x248 4x112x2 168 8x16x2144 X1, X2 0
Maximize π = 11x1 + 10x2 subject to the same constraints in Problem Minimize subject to c = 5y1 +4y2 7y + 8y2 168 14y+8y2224 2y+4y260 Ji, y2 > 0
(a) Convert the inequality constraints in the following data to equations by adding slack variables or subtracting surplus variables and express the equations in matrix form, (b) Determine the number
Minimize c = 3y1 + 2.5y2 subject to the same constraints in Problem Minimize c = 10y1 +5y2 subject to 4y 3y284 16y16y2 192 6y19y2180 y1, y2 0
Minimize c = 3y1 + 2.5y2 subject to the same constraints in Problem Minimize subject to c = 5y1 +4y2 7y + 8y2 168 14y+8y2224 2y+4y260 Ji, y2 > 0
Use graphs to solve the following linear programming problems. Minimize c = 10y1 +5y2 subject to 4y 3y284 16y16y2 192 6y19y2180 y1, y2 0
Minimize c = 30y1 + 25y2 subject to the same constraints in Problem 7.38. Minimize c = 12y1 + 20y2 subject to 4y5y2100 24y 15y2 360 2y 10y280 J1, J2 > 0
Use graphs to solve the following linear programming problems. Minimize c = 12y1 + 20y2 subject to 4y5y2100 24y 15y2 360 2y 10y280 J1, J2 > 0
Minimize c = 8y1 + 10y2 subject to the same constraints in Problem 7.36. Minimize subject to c = 7y1 +4y2 3y +2y248. 9y+4y2108- 2y1+5y2 65 Ji, y2 > 0
Use graphs to solve the following linear programming problems. Minimize subject to c = 7y1 +4y2 3y +2y248. 9y+4y2108- 2y1+5y2 65 Ji, y2 > 0
Maximize π = 15x1 + 6x2 subject to the same constraints in Problem 7.34. Minimize subject to c = 5y1 +4y2 7y + 8y2 168 14y+8y2224 2y+4y260 Ji, y2 > 0
Minimize c = 3y1 + 2.5y2 subject to the same constraints in Problem Maximize subject to =5x+4x2 7.5x15x2150 3x+4x2108 8x12x2 120 X1, X20
Redo Problem 7.20, given(b) With v = 5 and n = 2, 5 – 2 = 3 variables must be set equal to zero for a basic solution. Setting x1 = x2 = x3 = 0, the initial basic solution is s1 = 2 and s2 = 4.
Redo Problem 7.9, using the following data derived from Problem 7.2: Maximize =10x18x2 subject to 6x1 + 2x2 36 (constraint A) 3x1 +5x230 (constraint B) x1 + 4x2
Find the determinants of each of the following 2 × 2 matrices: 10 6 13 -9 16 (a) A = (b) B = 4 -5 11 -2 (c) C = - [ - 15 22 18 8 (d) D = -8 3 -9 -4
Compare with Problems 4.23 and Use matrix inversion to solve for Y and i, given IS: 0.4Y150i = 209 LM: 0.1Y250i = 35 Setting up the augmented matrix, 0.4 150 1 0 0.1 -250 0 1 1a. Multiplying row 1 by
Use Cramer’s rule to find the equilibrium values for x, y, and λ, given the following first-order conditions for constrained optimization in Problem 13.33:In matrix form, 14x-2y-=0 -2x+10y = 0
Use Cramer’s rule to find the equilibrium values for x, y, and λ, given the following first-order conditions for constrained optimization in Problem 13.21:Rearranging and setting in matrix form,
Use Cramer’s rule to solve for and in each of the following three interconnected markets:From Problem 4.14, the markets are simultaneously in equilibrium whenwhereSolving for P1, 2s1 = 6P1-8
Use Cramer’s rule to solve for the unknown variables in each of the following 3 × 3 systems of simultaneous equations. 209 150 |Ail = = 35 -250 209(-250)-150(35) = -57,500 |Al -57,500 and Y ==== =
Redo Problem 6.10 for a drop in autonomous investment, when A fall in autonomous investment leads to a drop in income and a decline in the interest rate. See Problem IS: 0.4Y+150i - 186 0 LM:
Use Cramer’s rule to solve for the equilibrium level of income and the interest rate , given IS: 0.3Y+100i 252 = 0 LM: 0.25Y - 200i 193 = 0
Use Cramer’s rule to solve for the unknown variables in each of the following 3 × 3 systems of simultaneous equations. Use Cramer's rule to solve for the equilibrium level of price P and quantity
Use Cramer’s rule to solve for the unknown variables in each of the following 3 × 3 systems of simultaneous equations. (b) 2a. Multiplying row 2 by - to obtain 1 in the a22 position, [ 1 8 0 ] 11
Use Cramer’s rule to solve for the unknown variables in each of the following 3 × 3 systems of simultaneous equations. la. Multiplying row 1 by to obtain 1 in the a11 position, 9 ] 1b.
Use Cramer’s rule to solve for the unknown variables in each of the following 3 × 3 systems of simultaneous equations. (a) 3x18x2+2x3 = 67 4x16x2+9x3 = 36 7x1+x2+5x3 = 49 3 8 2 A = 469 L7 1 Using
Use Cramer’s rule to solve for the unknown variables in each of the following 2 × 2 systems of simultaneous equations.Expressing the equations in matrix form,where Replacing the first column of A,
Find the determinants of each of the following 3 × 3 matrices: 2 7 8 (a) A = 6 3 5 -4 (b) B= 5 L1 4 9 3 962 27 -1 7 10 -2 3 8 0 (c) C = -4 5 8 (d) D=6 -4 7 0 9 6. 3 9 2
Use Cramer’s rule to solve each of the following equations: (a) 4x+5y=92 7x+6y= 128 (c) 2x-7y=-26 3x+5y=-8 (b) 13x4y = 29 (d) -8x+9y=41 - 6x + 7y = -244- 15x+8y = 202
Solve each of the following equations using Cramer’s rule: (a) 3x1+7x24x3 = 11 2x18x25x3 = 18 9x16x22x3 = 53 (c) 4x1-9x2-2x3 = 28 (b) 5x18x2 + 2x3 = -59 6x1 +4x2+7x3 = 52 -x1+9x2+4x3 = 90 8.X1 -
Using the data below derived from Problem 7.1,(1) Graph the inequality constraints by first solving each for x2 in terms of x1.(2) Regraph and darken in the feasible region.(3) Compute the slope of
A food processor wishes to make a least-cost package mixture consisting of three ingredients y1, y2, and y3. The first provides 4 units of carbohydrates and 3 units of protein and costs 25 cents an
A nutritionist wishes her clients to have a daily minimum of 30 units of vitamin A, 20 units of vitamin D, and 24 units of vitamin E. One dietary supplement yi costs $80 per kilogram ($80/kg)and
A game warden wants his animals to get a minimum of 36 milligrams (mg) of iodine, 84 mg of iron, and 16 mg of zinc each day. One feed y1 provides 3 mg of iodine, 6 mg of iron, and 1 mg of zinc; a
A carpenter makes three types of cabinets: provincial x1, colonial x2, and modern x3. The provincial model requires 8 hours for fabricating, 5 hours for sanding, and 6 hours for staining. The
A potter makes pitchers x1, bowls x2, and platters x3, with profit margins of $18, $10, and $12, respectively. Pitchers require 5 hours of spinning and 3 hours of glazing; bowls, 2 hours of spinning
A costume jeweler makes necklaces x1 and bracelets x2. Necklaces have a profit margin of $32;bracelets $24. Necklaces take 2 hours for stonecutting, 7 hours for setting, and 6 hours for
An aluminum plant turns out two types of aluminum x1 and x2. Type 1 takes 6 hours for melting, 3 hours for rolling, and 1 hour for cutting. Type 2 takes 2 hours for melting, 5 hours for rolling, and
A manufacturer makes two products x1 and x2. The first requires 5 hours for processing, 3 hours for assembling, and 4 hours for packaging. The second requires 2 hours for processing, 12 hours for
For each of following 2 × 2 matrices, find the determinant to determine whether the matrix issingular or nonsingular, and indicate the rank of the matrix..With |A| ≠ 0, A is nonsingular. Both rows
Use Cramer’s rule or matrix inversion to find the equilibrium level of income Ye and interest rate ie, given (a) IS: 0.35Y + 150i - 1409=0 LM: 0.2Y100i 794 = 0 - (b) IS: 0.25Y+175i 1757=0 - LM:
Use Cramer’s rule or matrix inversion to find the equilibrium price Pe and quantity Qe in each of the following markets: (a) Supply: 8P +16Q = 400 Demand: 5P+20Q = 710 (c) Supply: 30P + 6Q = -492
Find the inverse matrix for each of the following 3 × 3 matrices: 3 7 5 (a) A= 2 -8 5 (b) B = 6 4 27 2 9 6 -2 9 4 4 -9 -2 0 -4 (c) C=2 0 -7 (d) D= 8 0 -5 35 37 0 5 -8. 6 7 0
Find the inverse matrix for each of the following 2 × 2 matrices: (a) A = (c) C = 4 5 13 (b) B = 7 6 -8 9 2 -7 -6 7 (d) D = 3 5 15 8
For each of the following 3 × 3 matrices, find the determinant and indicate the rank of the matrix.Setting down the original matrix and to the right of it repeating the first two columns,Then
While matrix inversion has important uses in economic theory and the Gaussian elimination method is crucial for the simplex algorithm method of linear programming, practical problems are generally
Sales in millions of dollars have declined linearly from $905 in 1989 to $887.75 in 1992. On the basis of the trend, project the level of sales in 1995.
Growing at a constant rate, a firm’s costs have increased from $265 million in 1988 to $279 million in 1992. Estimate costs in 1996 if the trend continues.
How many tons of coal valued at $140 a ton should be mixed with coal worth $190 a ton to obtain a mixture of 32,000 tons of coal worth $175 a ton?
How much of a $50,000 account should a broker invest at 8 percent and how much at 12 percent to average a 9.5 percent yearly rate of return?
Determine the level of profit on sales of (a) 75 units and (b) 125 units for a company operating in a purely competitive market which receives $120 for each item sold and has a fixed cost of $1800
Estimate the total cost of producing (a) 10 units and (b) 100 units for a company with fixed costs of$85,000 and variable costs of $225 a unit.
A firm has fixed costs of $122,000 and variable costs of $750 a unit. Determine the firm’s total cost of producing (a) 25 units and (b) 50 units.
Estimate the current value after (a) 3 years and (b) 7 years of a printing press purchased for$265,000 and depreciating linearly by $32,000 a year.
Find the value after (a) 2 years and (b) 4 years of a photocopier which was purchased for $12,250 initially and is depreciating at a constant rate of $1995 a year.
Use the two-point formula to derive the equation for a straight line passing through:(a) (2, 6), (5, 18)(b) (−1, 10), (4, −5)(c) (−6, −3), (9, 7)(d) (4, −5), (10, −8)
Convert the following linear equations in standard form to the slope-intercept form:(a) 3x + 12y = 96(b) 12x – 16y = 240(c) 22x + 2y = 86(d) 28x – 4y = −104
Solve the following linear equations by using the properties of equality:(a) 6x – 7 = 3x + 2(b) 60 – 8x = 3x + 5(c) 7x + 5 = 4(3x – 8) + 7(d) 3(2x + 9) = 4(5x – 21) – 1

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