For the linear program Max 2A + 3B s.t. 1A+28 ≤4 SA+38 ≤ 15 A, B 20 find the optimal solution using the graphical solution procedure. What is the value of the objective function at the optimal solution? at (A, B) =
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- STAR Co. provides paper to smaller companies whose volumes are not large enough to warran paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The cutting patterns have been established: 1 2 Pattern 12ft. 15ft. 30ft. Trim Loss 0 4 1 10 ft. 3 0 7 ft. 8 0 0 4 ft. 2 1 2 1 ft. 5 2 3 1 1 ft. Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12)+1(15) + 2(30) = 99 hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. hand will be sold on the open market at the selling price. No inventory is held. Number of: 3Chikana Company produces and sells rattan baskets. The number of drifts produced are the corresponding total production costs for six months, which are representatives for the year, are as follows: Month Units Produced Production Costs P 4,000 8,000 6,000 7,500 8,500 7,250 April Мay 500 700 June 900 July August September 600 800 550 Required: Solve for the variable and fixed cost component using: a.) High- Low Method b.) Least- Squares RegressionLPP Model Maximize P = 12x + 10y Subject to : 4x + 3y < 480 2x + 3y < 360 X, y 2 0 Which of the following points (x, y) is feasible? A) ( 120, 10) B ( 30, 100 ) c) ( 60, 90 ) D) ( 10, 120 )
- For minimization linear programming problem, the simplex method is terminated when all values of: a. Z (NB) s0 Ob. None of them Z (NB) = 0 Z (NB) 2 02(a) The tableau is not optimal for either maximization or a minimization problem. Thus, when a non-basic variable enters the solution it can either increase or decrease Z or leave it unchanged, depending on the parameters of the entering non basic variable. Basic x1 X2 X3 X4 X5 X6 X7 X8 solution -5 4 -1 -10 620 X8 3 -2 -3 -1 1 12 X3 1 1 3 1 3 X1 1 -1 -4 (i)Categorize the variables as basic and non-basic and provide the current values of all the variables. (ii)Assuming that the problem is of the maximization type, identify the non- basic variables that have the potential to improve the value of Z. If each such 3 variable enters the basic solution, determine the associated leaving variable, if any, and the associated change in Z. (iii)Repeat part (b) assuming that the problem is of the minimization type. (iv)Which non basic variable(s) will not cause a change in the value of Z when selected to enter the solution? (b) Let xij be the amount shipped from source i to destination j in a 5X5…a. Which of the following best describes the meaning of the equation P(25) = 200? 1. When 200 calculators are sold, the profit is $25. II. When 200 calculators are sold, the profit is increasing at a rate of $25 per additional calculator III. When 25 calculators are sold, the profit is $200. IV. When 25 calculators are sold, the profit is increasing at a rate of $200 per additional calculato
- Suppose we are solving a maximization problem andthe variable xr is about to leave the basis.a What is the coefficient of xr in the current row 0?b Show that after the current pivot is performed, thecoefficient of xr in row 0 cannot be less than zero.c Explain why a variable that has left the basis on agiven pivot cannot re-enter the basis on the next pivot.Determine the pivot element in the simplex tableau. (If there is more than one correct pivot element, choose the element with the smaller row number.) X1 X2 X3 S1 S2 3 4 2 1 15 1 20 -8 -3 10 1 row column N O OUsing back-substitution, show that an ARMA(1, 1) model may be written as eitheran AR or an MA model.
- Aa6. please solve with formulas not excellInnis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%. The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis' risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3. The higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis's client also specified that at least $300,000 be invested in the money market fund. Refer to the computer solution shown below. Optimal…Consider the linear program max 4y_{1} + 5y_{2} s.t. - y_{1} + y_{2} <= 4 y_{1} - y_{2} <= 10 y_{1}, y_{2} >= 0 (a) Show graphically that the model is unbounded.