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%.minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2The 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 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. The sales price is 5 dollars for each pie. What is the fixed costs of making 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?
- MaximizationProblems 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.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 - 3x2
- 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) 3Formulate the situation as a system of inequalities. (Let x represent the number of dinghies the company can manufacture and y represent the number of rowboats.) A boat company manufactures aluminum dinghies and rowboats. The hours of metal work and painting needed for each are shown in the table, together with the hours of skilled labor available for each task. How many of each kind of boat can the company manufacture? (hours) Dinghy Rowboat Labor Available Metal Work 2 3 108 Painting 2 2 90 (labor for metal work) (labor for painting) x ≥ 0, y ≥ 0