Use the Big M method, work through the simplex method step by step to solve the following problem. Maximize Z = 4x₁ + 2x₂ + 3x3 + 5x4, subject to 2x₁ + 3x₂ + 4x3 + 2x4 = 300 8x₁ + x₂ + x3 + 5x4 = 300 and x₁0, X₂ ≥ 0, X3 ≥ 0, x4 ≥ 0.
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- If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.The Math Club is selling pies on March 14th as a fundraiser. Let Q be the number of pies they make and sell. The total cost, C(Q) in dollars, for making Q pies is given by: C(Q) = 36 + 2Q. The sales price is 5 dollars for each pie. What is the fixed costs of making pies?minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2
- The Math Club is selling pies on March 14th as a fundraiser. Let Q be the number of pies they make and sell. The total cost, C(Q) in dollars, for making Q pies is given by: C(Q) = 36 + 2Q. Sales price is 5 dollars for each pie. What is the additional cost to make 21 pies instead of 20 pies?The Math Club is selling pies on March 14th as a fundraiser. Let Q be the number of pies they make and sell. The total cost, C(Q) in dollars, for making Q pies is given by: C(Q) = 36 + 2Q. Sales price is 5 dollars for each pie. What is the total cost of making 20 pies?The original z-score formula intended for public manufacturing companies is shown below: Altman Z-Score = (1.2 × X1) + (1.4 × X2) + (3.3 × X3) + (0.6 × X4) + (0.99 × X5) The inputs for our z-score calculation are the following: X1 = Working Capital ÷ Total Asset X2 = Retained Earnings ÷ Total Assets X3 = EBIT ÷ Total Assets X4 = Market Capitalization ÷ Total Liabilities X5 = Sales ÷ Total Assets The following assumptions will be used for our modeling exercise. Current Assets = $60 million Current Liabilities = $40 million Fixed Assets = $100 million Net Income = $10 million Dividends = $2 million Sales = $60 million COGS and SG&A = $40 million P/E Multiple = 8.0x Total Liabilities = $120 million What is the Z-score?
- 4 For each of the following, determine the direction in which the objective function increases: a z = 4x, - x2 b z = -x, + 2x2 C z = -x - 3x2MaximizationProblems and Minimization problems ***When using the simplex method, what is the difference between maximizing and minimizing?You estimate that your cattle farm will generate $1 million of profits on sales of $5.4 million under normal economic conditions and that the degree of operating leverage is 8. What will profits be if sales turn out to be $4.7 million? Note: Negative amount should be indicated by a minus sign. Round your answer to 1 decimal place. What if they are $6.1 million? Note: Round your answer to 1 decimal place.
- What combination of x and y will yield the optimum for this problem? Maximize Z = $3x + $15y Subject to: Multiple Choice x= 0, y=4 x= 0, y=3 x= 0, y=0 x= 2y=0 O x=1,y=25 2x + 4y ≤ 12 5x + 2y ≤ 10A simplex tableau is shown below. You should complete the tableau and respond to the questions posed. Basis CB cj JIN Cj Zj X1 3 1 X2 4 x3 0 0 5 1/2 0 1 S1 O 1/2 S2 O -1/2 6 -1/4 1 What is the current value of the objective function of the current simplex tableau? (round to 2 decimal places) 3Use the graphical 2-D method to maximize subject to If there are no solutions, enter None for z. Maximum value is z = where x1 = and x2 = x1 3x1 X1 z = 6x1 + 2x2 + X2 + 4x2 + 3x2 X1 ≥ 0 > 21 72 <44 X2 ≥ 0