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- Solve the question below using the attached excel templates with formulas for renting both slow and fast copies (labeled in the excel tabs). Question: The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee’s time is worth $15 per hour. The slow copier rents for $4 per hour, and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15 per hour, and it takes an employee an average of six minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine are exponentially distributed.) Which machine should the department rent to minimize expected total cost per hour?TRUE OR FALSE The simplex method is a linear programming procedure designed to handle only three variablesInstruction: Answer the following systematically. Strictly follow the format of the solution (Example problem + complete solution is provided in the photos below). I WON'T LIKE YOUR ANSWER IF IT IS NOT PROPERLY FOLLOWED AND INCORRECT) A small generator burns two types of fuel – low sulfur and high sulfur – to produce electricity. For one hour, each gallon of low sulfur emits 3 units of sulfur dioxide, generates 4 kilowatts electricity, and cost P600. Each gallon of high sulfur emits 5 units of sulfur dioxide, generates 4 kilowatts, and costs P500. The Environmental Protection Agency insists that the maximum amount of sulfur dioxide that can be emitted per hour is 15 units. Suppose that at least 16 kilowatts must be generated per hour, how many gallons of low sulfur and how many gallons of high sulfur must be utilized per hour to minimize the cost of fuel? Objective: minimize
- Which of the following is not an assumption of a maximum flow problem? Multiple Choice All flow through the network originates at one node, called the source. If a node is not the source or the sink then it is a transshipment node. Flow can move toward the sink and away from the sink. The maximum amount of flow through an arc is given by the capacity of the arc. The objective is to maximize the total amount of flow from the source to the sink.A public hospital employs volunteers to attend the reception between 8:00 A.M. and 10:00 P.M. Each volunteer works three consecutive hours, except those who enter at 8:00 P.M., who only work 2 hours. An approximation to the minimum need for volunteers is through a staggered function in two-hour intervals, which start at 8:00 A.M. and they are 4, 6, 8, 6, 4, 6 and 8 volunteers per interval. As most of the volunteers are pensioners, they are willing to offer their services at any time of the day (8:00 A.M. to 10:00 P.M.). However, as most charities compete for your services, the amount required should be kept as low as possible. Determine an optimal schedule of start time and number of volunteers.An experiment that involves learning in animals requires placing white mice and rabbits into separate, controlled environments: environment I and environment II. The maximum amount of time available in environment I is 420 minutes, and the maximum amount of time available in environment II is 624 minutes. The white mice must spend 10 minutes in environment I and 24 minutes in environment II, and the rabbits must spend 12 minutes in environment I and 16 minutes in environment II. (a) Write a system of inequalities that describes the constraints on the number of each type of animal used in the experiment. (Let x represent the number of mice, and let y represent the number of rabbits.) environment I time constraint environment II time constraint x ≥ 0 experiment constraint, mice y ≥ 0 experiment constraint, rabbits (b) Graph the solution of the system of inequalities and find the corners of the solution region.
- A company produces three different products; x,y, and z. For the production of 1 unit of product x, 1 unit of A and 1 unit of B are used as input. 1 unit of A and 2 units of B are used to produce 1 unit of product y. To produce 1 unit of product z, only 1 unit of A is used. The company holds 40 units of A and 20 units of B periodically in total. By the way, the company can not produce product y more than the twice of product z. On the other hand, the sale price of 1 unit of product x is 10 TL, product y is 15 TL and product z is 12 TL. Furthermore, the cost of 1 unit of product x is 8 TL, product y is 9 TL and product z is 7 TL. According to above information, what should be the company’s optimal product mix to maximize its profit? Construct the problem as a Linear programming model. Solve the above problem by using Simplex Method.Which of the following is not involved in a linear programming problem? a. variable b. solution set c. objective function d. condition The statement |x| = -x is true if: a. x≥0 b. x≤0 c. x ≠0 d. x>0A linear programming computer package is needed. Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company's needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows. Component Supplier 1 2 3 1 $11 $12 $13 2 $9 $10 $9 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows. Supplier 1 2 3 Capacity 700 1,100 900 (a) If the Edwards production plan for the next period includes 1,100 units of component 1 and 900 units of component 2, what purchases do you recommend? That is,…
- TRUE OR FALSE Each constraint excluding nonnegativity constraints, in the mathematical formulation of a linear program generates one row in the simplex table.A linear programming computer package is needed. Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company's needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows. Component Supplier 1 2 3 1 $13 $14 $15 2 $11 $12 $11 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows. Supplier 1 2 3 Capacity 500 900 700 If the Edwards production plan for the next period includes 900 units of component 1 and 700 units of component 2, what purchases do you recommend? That is, how many…. A commercial orchard grows, picks, and packs apples and pears. A peck (quarter bushel) of apples takes 4 minutes to pick and 5 minutes to pack; a peck of pears takes 5 minutes to pick and 4 minutes to pack. Only one picker and one packer are available. How many pecks each of apples and pears should be picked and packet every hour (60 minutes) if the profit is $3/peck for apples and $2/peck for pears? Solve graphically as a linear program and confirm analytically.