Please develop a linear programming model for the problem. b. Find the optimal solution via Excel. (showing formulas and steps if possible)
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Big Lots Services (BLS) would like to develop a model that will help allocate their technician’s time between service calls to regular contract customers and new customers. A maximum of eighty hours of technician time is available over the two-week planning period. To satisfy cash flow requirements, at least eight hundred dollars in revenue (per technician) must be generated during the two-week period. Technician time for regular customers generates twenty-five dollars per hour. However, technician time for new customers only generates an average of eight dollars per hour. To ensure that new customer contracts are being maintained, the technician time spent on new customer contracts must be at least sixty percent of the time spent on regular customer contracts. Given these revenue and policy requirements, (BLS) would like to determine how to allocate technician time between regular customers and new customers so that the total number of customers contracted during the two week period will be maximized. Technicians require an average of fifty minutes for each regular customer contract and one hour for each new customer contract.
a. Please develop a linear programming model for the problem.
b. Find the optimal solution via Excel. (showing formulas and steps if possible)
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- Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?Management of High Tech Services (HTS) would like to develop a model that will help allocate its technicians’ time between service calls to regular contract customers and new customers. A maximum of 90 hours of technician time is available over the two-week planning period. To satisfy cash flow requirements, at least $950 in revenue (per technician) must be generated during the two-week period. Technician time for regular customers generates $40 per hour. However, technician time for new customers only generates an average of $6 per hour because in many cases a new customer contact does not provide billable services. To ensure that new customer contacts are being maintained, the technician time spent on new customer contacts must be at least 50% of the time spent on regular customer contacts. Given these revenue and policy requirements, HTS would like to determine how to allocate technician time between regular customers and new customers so that the total number of customers contacted…A call center employs 1,425 agents. Every month 57 employees leave the company and 57 new employees are hired. a. How long on average does an agent work for this call center (in months) Suppose the cost of hiring and training a new agent is $1,140. The manager of this call center believes that increasing agents’ salaries would keep them working longer at the company. The manager wants to increase the average time that an agent works for the call center to 36 months, or three years. b-1. Given the current average working time for agents at this call center, determine the current annual cost for hiring and training. b-2. Assuming the average time that an agent works for the call center is increased to 36 months, determine the new annual cost for hiring and training. b-3. If the time an agent works for the call center is increased to 36 months on average, how much could the company save on hiring and training costs over a year?
- Management of High Tech Services (HTS) would like to develop a model that will help allocate its technicians' time between service calls to regular contract customers and new customers. A maximum of 90 hours of technician time is available over the two-week planning period. To satisfy cash flow requirements, at least $900 in revenue (per technician) must be generated during the two-week period. Technician time for regular customers generates $30 per hour. However, technician time for new customers only generates an average of $9 per hour because in many cases a new customer contact does not provide billable services. To ensure that new customer contacts are being maintained, the technician time spent on new customer contacts must be at least 80% of the time spent on regular customer contacts. Given these revenue and policy requirements, HTS would like to determine how to allocate technician time between regular customers and new customers so that the total number of customers contacted…Management of High Tech Services (HTS) would like to develop a model that will help allocate its technicians' time between service calls to regular contract customers and new customers. A maximum of 90 hours of technician time is available over the two-week planning period. To satisfy cash flow requirements, at least $900 in revenue (per technician) must be generated during the two-week period. Technician time for regular customers generates $30 per hour. However, technician time for new customers only generates an average of $9 per hour because in many cases a new customer contact does not provide billable services. To ensure that new customer contacts are being maintained, the technician time spent on new customer contacts must be at least 80% of the time spent on regular customer contacts. Given these revenue and policy requirements, HTS would like to determine how to allocate technician time between regular customers and new customers so that the total number of customers contacted…The Tiny Toy Company makes three types of new toys: the tiny tank, the tiny truck, and the tiny turtle. Plastic used in one unit of each is 1.5, 2.0 and 1.0 pounds, respectively. Rubber for one unit of each toy is 0.5, 0.5, and 1.0 pounds, respectively. Also, each tank uses 0.3 pounds of metal and the truck uses 0.6 pounds of metal during production. The average weekly availability for plastic is 16,000 pounds, 9,000 pounds of metal, and 5,000 pounds of rubber. It takes two hours of labor to make one tank, two hours for one truck, and one hour for a turtle. The company allows no more than 40 hours a week for production (priority #1). Finally, the cost of manufacturing one tank is $7, 1 truck is $5 and 1 turtle is $4; a target budget of $164,000 is initially used as a guideline for the company to follow. Minimize over-utilization of the weekly available supply of materials used in making the toys and place twice as much emphasis on the plastic (priority #2) Minimize the under and…
- The Tiny Toy Company makes three types of new toys: the tiny tank, the tiny truck, and the tiny turtle. Plastic used in one unit of each is 1.5, 2.0 and 1.0 pounds, respectively. Rubber for one unit of each toy is 0.5, 0.5, and 1.0 pounds, respectively. Also, each tank uses 0.3 pounds of metal and the truck uses 0.6 pounds of metal during production. The average weekly availability for plastic is 16,000 pounds, 9,000 pounds of metal, and 5,000 pounds of rubber. It takes two hours of labor to make one tank, two hours for one truck, and one hour for a turtle. The company allows no more than 40 hours a week for production (priority #1). Finally, the cost of manufacturing one tank is $7, 1 truck is $5 and 1 turtle is $4; a target budget of $164,000 is initially used as a guideline for the company to follow. a) Minimize over-utilization of the weekly available supply of materials used in making the toys and place twice as much emphasis on the plastic (priority #2) b) Minimize the under…The Tiny Toy Company makes three types of new toys: the tiny tank, the tiny truck, and the tiny turtle. Plastic used in one unit of each is 1.5, 2.0 and 1.0 pounds, respectively. Rubber for one unit of each toy is 0.5, 0.5, and 1.0 pounds, respectively. Also, each tank uses 0.3 pounds of metal, and the truck uses 0.6 pounds of metal during production. The average weekly availability for plastic is 16,000 pounds, 9,000 pounds of metal, and 5,000 pounds of rubber. It takes two hours of labor to make one tank, two hours for one truck, and one hour for a turtle. The company allows no more than 40 hours a week for production (priority #1). Finally, the cost of manufacturing one tank is $7, 1 truck is $5 and 1 turtle is $4; a target budget of $164,000 is initially used as a guideline for the company to follow. a) Minimize over-utilization of the weekly available supply of materials used in making the toys and place twice as much emphasis on the plastic (priority #2) b) Minimize the…Rienzi Farms grows sugar cane and soybeans on its 500 acres of land. An acre of soybeans brings a $1000 contribution to overhead and profit; an acre of sugar cane has a contribution of $2500. Because of a government program no more than 150 acres may be planted in soybeans. During the planting season 1800 hours of planting time will be available. Each acre of soybeans requires 2 hours, while each acre of sugar cane requires 6 hours. The company seeks maximum contribution from its planting decision. a) Formulate the problem as a linear program. b) Solve using the corner-point method (graphical method).
- A car wash offers two different types of wash services, deluxe wash and standard wash. The deluxe wash require(s) three steps: pre-wash, wash and dry. The standard wash only require(s) two steps: wash and dry. The pre-wash step has a capacity of 7 cars per hour. The wash step has a capacity of 11 cars per hour. The dry step has a capacity of 10 cars per hour. The demand for deluxe wash is 7 cars per hour and the demand for standard wash is 11 cars per hour. Instruction: Round to the nearest integer percentage. What is the implied utilization of the bottleneck resource?A furniture company manufactures chairs and desks. The sawing department cuts the lumber for both products, which is then sent to separate assembly departments. Assembled items are sent to the painting department for finishing. The daily capacity of the sawing department is 200 chairs or 80 desks. The chair assembly department can produce 120 chairs daily, and the desk assembly department 60 desks daily. The paint department has a daily capacity of either 150 chairs or 100 desks. Given that the profit per chair is $50 and that of a desk is $100. Formulate the problem as a linear program to determine the optimal product mix for the company.A software support company has the following minimum personnel requirements “on duty” during the week. Each employee is required to have two consecutive days off. What are the minimum total regular employees required to satisfy the requirements? (Assume, because of accounting reasons, no employee can take Sunday and Monday off).