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- Show the complete Linear Programming Model. Show solutions (i.e. decision variables, objective function, subject to constraints, etc.) Q. A gold processor has two sources of gold ore, source A and source B. In order to keep his plant running, at least three tons of ore must be processed each day. Ore from source A costs $1,000 per ton to process, and ore from source B costs $500 per ton to process. Costs must be kept to less than $4,000 per day. Moreover, Government Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints? Formulate the LP model.Consider the following linear programming model: maximize Z = 3x1 + 2x2 subject to : x1 +x2 ≤ 1 x1 + x2 ≥ 2 x1,x2 ≥ 0 a) Write this model in a standard (augmented) form. (i.e. Introduce slack/surplus, artificial etc.)b) Constract the initial simplex tableau and carry on your calculations to solve this model using the simplex method. Interpret your result.Suppose a company must service customers lying inan area of A sq mi with n warehouses. Kolesar and Blumhave shown that the average distance between a warehouseand a customer is An Assume that it costs the company $60,000 per year tomaintain a warehouse and $400,000 to build a warehouse.(Assume that a $400,000 cost is equivalent to foreverincurring a cost of $40,000 per year.) The company fills160,000 orders per year, and the shipping cost per order is$1 per mile. If the company serves an area of 100 sq mi,then how many warehouses should it have?
- Find the minimum value of the function z=2x+2y subject to the following constraints. x≤17 y≤16 5x+2y≥42 3x+11y≥844.Problem in the Image Please solve with the long anlysis explain and clearly27 In order to manufacture 3,000 pairs of shoes in a week, a firm can use 3,000 workers and 100 machines or 200 machines and 4,000 workers Which method is considered more technically efficient? a 4,000 workers and 200 machines b Both are equally efficient c 3,000 workers and 100 machines d Neither could be considered efficient 33 A manufacturing business can use 100 workers and 20 machines, 140 workers and 18 machines, or 150 workers and 18 machines to produce 80 chairs If each worker costs $40 and each machine is rented for $1000, the economically efficient input combination is: a 100 workers and 20 machines b 150 workers and 18 machines c none of these input combinations d 140 workers and 18 machines
- 2. A firm makes two products, Y and Z. Each unit of Y costs $10 and sells for $40. Each unit of Z costs $5 and sells for $25. If the firm's goal is to maximize profit, what would be the appropriate objective function? Select one: a. Maximize profit Z = $10Y + $25Z b. Maximize profit Z = 0.25Y + 0.20Z c. Maximize profit Z = $40Y + $25Z d. Maximize profit Z = $50(Y + Z) e. Maximize profit Z = $30Y + $20Z2. A firm makes two products X and Y and has a total production capacity of 9 tons per day.X and Y requiring the same production capacity. The same has a permanent contract to supply at least two tons of X and at least 3 tons of Y per day to another company. Each ton of X requires 20 machine hours of production time and each ton of Y requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. The entire firm's output can be sold and profit made is 80 R.O of X and 120 R.O per ton of Y. It is required to determine the production schedule for maximum profit and to calculate this profit. Formulate a LPP.9. Which of the following is NOT a requirement of a linear programming problem? Select one: a. constraints, expressed as linear equations or inequalities b. an objective function to be maximized or minimized c. an objective function, expressed in linear terms d. alternative courses of action e. one constraint for each decision variable
- With the use of illustrations or examples, explain the following terms:a) Slack variableb) Surplus variablec) Constraintsd) Non-negative constraintse) Objective function NB: Answer question a-edo not need to solve thr problem, jsit crrate the linear program.(b) A company produces 3 products A, B and C processed on 3 machines P, Q, R before completion. Machine P can process 25 units of A or 50 unit of B or 75 units of C per hour. Machine Q can process 50 units of any of the products per hour. Machine R can process 50 units of A or 25 unit of B or 100 units of C per hour. The processing hours available on machines P, Q and R are 12, 12 and 13 respectively. Use matrix method, find (i) How many units of each of the three products can be produced per day (ii) The production cost per unit, if cost per hour of operating machines A,B and C are N$500, N$1,000 and N$1,500 respectively. (iii) The total cost of production.