Use branch-and-bound to solve the following IP max z = 2x₁ + 3x₂ s.t. x₁ + 2x₂ = 10 3x₁ + 4x₂ 25 X1, X₂ = 0; X₁, X₂ integer
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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: 3Please do not give solution in image formate thanku. Consider a firm that operates a cannery. All fish brought in by a fleet of fishing boats are processed at the cannery. The firm also has a freezer of unlimited size that stores unprocessed fish. Assume that the freezer is empty in the beginning of the year. There are three seasons. The fleet yields 8400 tons/month during the first third of the year, 11200 tons/month during the middle third, and only 1400 tons/month during the final third. The cannery's processing capacity equals 7000 tons/month. a- What is the inventory level at the end of January? Please give your answer in tons. b - What is the inventory level at the end of February? Please give your answer in tons. c - What is the inventory level at the end of May? Please give your answer in tons. d - What is the average monthly inventory (in tons)? Please keep 4 decimals. e - Calculate the average system throughput rate. Please give your answer in tons/month. f - Determine the…What is the meaning of -1 "ij m = K¡Yi, for i = 1, 2, n? %3D %3D .... j=1 For each facility, the total quantity sent out cannot exceed its capacity, and no quantity is shipped if the facility is not open. For each facility, the total quantity sent out cannot exceed its capacity. For each facility, no quantity is shipped if the facility is not open. The total quantity sent from facility i cannot exceed its capacity, and no quantity is shipped if facility i is not open.
- write a linear program that will maximize profits. You don’t need to solve it. Hint: Define your variables as: Xij = tons of commodity i loaded into cargo hold j2. An infinite sheet of uniform charge ps (C/m^2) is placed at z=0. Use Gauss' law to calculate the electric field at a distance z created by the sheet.A company possesses two manufacturing plants, each of which can produce three products, X, Y, and Z, from a common raw material. However, the proportion in which the products are produced differs in each plant, and so are plant's operating costs per hour. Data on production per hour and costs are given below, together with current orders in hand of each product. Products Operating cost per hour Y Plant A 4 9. Plant B 4 2 10 Orders on hand 50 24 60 Formulate the above as a linear programming problem. Find the number of production hours needed to fulfill the orders on hand at minimum cost using the using Big M method.
- LPP 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 )OPEC Explain the significance of the following variables with reference to linear programming problem: Entering variable Leaving variableAt a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be more economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the end of year i and trading it in at the end of year j (where year O is now). i 012 1 $13,000 j 2 $28,000 $17,000 3 $48,000 $33,000 $20,000 The problem is to determine at what times (if any) the tractor should be replaced to minimize the total cost for the tractors over 3 years. (a) Formulate this problem as a minimum cost flow problem by showing the…