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32_ FALSE

33_ 4

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W1 Assignment: True or False

W1 Assignment: True or False

If you think the statement is true, then prove it. On the other hand, if you think the statement is false, then give an example that disproves the statement. For example, the statement "If a and b are real numbers, then a - b = b - a" is false and an example that disproves it may be constructed by taking a = 3 and b = 5. For these values of a and b, we find a - b = 3 - 5 = -2 but b - a = 5 - 3 = 2 and this shows that a - b ≠ b - a. Such an example is called a ≠counterexample.True or false. The slope of a horizontal line is undefined.True or false. Suppose the slope of a straight line L is -3/4 and P is a given point on L. If Q is a point on L lying 2 units to the right of P, then Q is situated 3/2 units below P.True or false. The y-intercept of the straight line with equation Ax + By + C = 0 is -C/B (B ≠ 0).True or false. If a line L1 has equation y = mx + b, where m and b are constants with m ≠ 0,then an equation of a line L2 perpendicular to L1 has the form , where C is a constant.True or false. Suppose an asset is being depreciated linearly. Then the rate of depreciation of the asset is given by the negative of the slope of the depreciation line.True or false. If R and C are linear revenue and cost functions, respectively, and (x0, p0) is the breakeven point, then P(x) > P(x0) if x > x0, where P is the profit function.True or false. The least-squares line must pass through at least one of the data points.

W2 Assignment: True or False

W2 Assignment: True or False

If you think the statement is true, then show that it is true. On the other hand, if you think the statement is false, then give an example that disproves the statement. For example, the statement "If A and B are matrices of the same order, then A - B = B - A" is false and an example that disproves it is For while Such an example is called a counterexample.True or false: A system comprising two linear equations in two variables has a unique solution if and only if the straight lines represented by the equations are nonparallel.True or false: Suppose the straight lines represented by a system of two linear equations in two variables are parallel to each other. Then the system has infinitely many solutions.True or false: If A and B are matrices of the same order, then .True or false: If A and B are matrices such that AB and BA are both defined, then A and B must be square matrices.True or false: If A is a square matrix with inverse and c is a nonzero real number, then .True or false: If AX = B is a system of n linear equations in n unknowns and does not exist, then AX = B does not have a unique solution.

W3 Assignment: True or False

W3 Assignment: True or False

True or false. If all the coefficients a1, a2, …, an in the objective function P = a1x1 + a2x2 + … + anxn are nonpositive, then the only solution of the problem is x1 = x2 = … = xn and P = 0.True or false. The pivot column of a simplex tableau identifies the variable whose value is to be decreased in order to increase the value of the objective function (or at least keep it unchanged).True or false. The ratio associated with the pivot row tells us by how much the variable associated with the pivot column can be increased while the corresponding point still lies in the feasible set.True or false. At any iteration of the simplex procedure, if it is not possible to compute the ratios or the ratios are negative, then one can conclude that the linear programming problem has no solution.True or false. If the last row to the left of the vertical line of the final simplex tableau has a zero in a column that is not a unit column, then the linear programming problem has infinitely many solutions.True or false. Suppose you are given a linear programming problem satisfying the conditions:The objective function is to be minimized. All the variables involved are nonnegative, and Each linear constraint may be written so that the expression involving the variables is greater than or equal to a negative constant.Then the problem can be solved using the simplex method to maximize the objective function P = -C.True or false. The objective function of the primal problem can attain an optimal value that is different from the optimal value attained by the dual problem.

W5 Assignment: True or False

W5 Assignment: True or False

True or false. When simple interest is used, the accumulated amount is a linear function of time.True or false. Compound interest that is converted once a year is the same as simple interest.True or false. If interest is compounded annually, then the effective rate of interest is the same as the nominal rate of interest.True or false. The present value is always smaller than the future value.True or false. The future value of an annuity can be found by adding together all the payments that are paid into an account.True or false. The periodic payment R where and P is the loan amount and i is the interest per period that will amortize the loan at the end of the term comprising n periods.True or false. A sinking fund is the accumulated amount to be realized at some future date (the end of the term) when a fixed number of periodic payments are paid into an account earning interest at the rate of i per period.

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