Project Design The Megabuck Hospital Corporation is to build a state-subsidized nursing home serving homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 1,000 homeless patients and no more than 750 high-income patients in order to qualify for state subsidies. The overall capacity of the nursing home is to be 2,1 00 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high income patients. Because of the state subsidy, the nursing home will make an average profit of $10,000 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $8,000 per month. How many of each type of patient should the nursing home house to maximize profit? [HINT: See Example 3.]
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Finite Mathematics
- If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.arrow_forwardIf the cost of each Robust tablet increases to 75 c and the cost of each Vigortab increases to 80 c , find the minimum cost.arrow_forwardDr. Maureen Becker, the head administrator at Jefferson County Regional Hospital, must determine a schedule for nurses to make sure there are enough of them on duty throughout the day. During the day, the demand for nurses varies. Maureen has broken the day into twelve 2-hour periods. The slowest time of the day encompasses the three periods from 12:00 a.m. to 6:00 a.m., which, beginning at midnight, require a minimum of 30, 20, and 40 nurses, respectively. The demand for nurses steadily increases during the next four daytime periods. Beginning with the 6:00 a.m.–8:00 a.m. period, a minimum of 50, 60, 80, and 80 nurses are required for these four periods, respectively. After 2:00 p.m. the demand for nurses decreases during the afternoon and evening hours. For the five 2-hour periods beginning at 2:00 p.m. and ending at midnight, 70, 70, 60, 50, and 50 nurses are required, respectively. A nurse reports for duty at the beginning of one of the 2-hour periods and works 8 consecutive hours…arrow_forward
- Dr. Maureen Becker, the head administrator at Jefferson County Regional Hospital, must determine a schedule for nurses to make sure there are enough of them on duty throughout the day. During the day, the demand for nurses varies. Maureen has broken the day into twelve 2-hour periods. The slowest time of the day encompasses the three periods from 12:00 a.m. to 6:00 a.m., which, beginning at midnight, require a minimum of 30, 20, and 40 nurses, respectively. The demand for nurses steadily increases during the next four daytime periods. Beginning with the 6:00 a.m.–8:00 a.m. period, a minimum of 50, 60, 80, and 80 nurses are required for these four periods, respectively. After 2:00 p.m. the demand for nurses decreases during the afternoon and evening hours. For the five 2-hour periods beginning at 2:00 p.m. and ending at midnight, 70, 70, 60, 50, and 50 nurses are required, respectively. A nurse reports for duty at the beginning of one of the 2-hour periods and works 8 consecutive hours…arrow_forwardThe Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 700 homeless patients and no more than 620 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $13,000 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $9,000 per month. How many of each type of patient should it house in order to maximize profit?arrow_forwardThe Megabuck Hospital Corp. is to build a state-subsidized nursing home catering to homeless patients as well as high-income patients. State regulations require that every subsidized nursing home must house a minimum of 750 homeless patients and no more than 900 high-income patients in order to qualify for state subsidies. The overall capacity of the hospital is to be 1,800 patients. The board of directors, under pressure from a neighborhood group, insists that the number of homeless patients should not exceed twice the number of high-income patients. Due to the state subsidy, the hospital will make an average profit of $9,500 per month for every homeless patient it houses, whereas the profit per high-income patient is estimated at $8,000 per month. How many of each type of patient should it house in order to maximize profit? HINT [See Example 3.] (If an answer does not exist, enter DNE.) high-income patients: homeless: profit:arrow_forward
- A furniture store expects to sell 120 coffee tables during the next year. It costs $1.50 to store one coffee table for one year. To reorder, there is a fixed cost of $10, plus $2.80 for each coffee table ordered. In what lot size and how many times per year should an order be placed to minimize inventory costs? coffee tables per order orders per yeararrow_forwardMcJester's Burger Hut plans to expand by opening several new restaurants. The chain operates two types of restaurants: drive-through and full-service. • A drive-through restaurant costs $111,000 to construct, requires 7 employees, and has an expected annual revenue of $205,000. . A full-service restaurant costs $184,000 to construct, requires 17 employees, and has an expected annual revenue of $565,000. . McJester's has $3,250,000 in capital available for expansion. • Labor contracts require that they higher no more than 325 employees. • Licensing restrictions require that they open no more than 25 new restaurants. Let a be the number of drive-through restaurants and let y be the number of full-service restaurants in this expansion. Let R be the expected annual revenue in dollars resulting from the expansion. McJester's wants to maximize the expected revenue. Set up the linear programming problem. Answer the following questions about this linear programming problem.arrow_forwardSoutheastern Oklahoma State University's business program has the facilities and faculty to handle an enrollment of 2,100 new students per semester. However, in an effort to limit class sizes to a "reasonable" level (under 200, generally), Southeastern's dean, Holly Lutze, placed a ceiling on enrollment of 1,800 new students. Although there was ample demand for business courses last semester, conflicting schedules allowed only 1,450 new students to take business courses. The utilization rate for Southeastern =% (enter your response as a percentage rounded to one decimal place). The efficiency rate for Southeastern =% (enter your response as a percentage rounded to one decimal place).arrow_forward
- Dr. Maureen Becker, the head administrator at Jefferson County Regional Hospital, must determine a schedule for nurses to make sure there are enough of them on duty throughout the day. During the day, the demand for nurses varies. Maureen has broken the day into twelve 2hour periods. The slowest time of the day encompasses the three periods from 12:00 A.M. to 6:00 A.M., which, beginning at midnight, require a minimum of 30, 20, and 40 nurses, respectively. The demand for nurses steadily increases during the next four daytime periods. Beginning with the 6:00 A.M.–8:00 A.M. period, a minimum of 50, 60, 80, and 80 nurses are required for these four periods, respectively. After 2:00 P.M. the demand for nurses decreases during the afternoon and evening hours. For the five 2-hour periods beginning at 2:00 P.M. and ending at midnight, 70, 70, 60, 50, and 50 nurses are required, respectively. A nurse reports for duty at the beginning of one of the 2-hour periods and works 8 consecutive hours…arrow_forwardThe Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown. To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized. Given the promotional budget is $18,200, formulate the linear programming problem.arrow_forwardHoosier Power needs to determine a capacity expansion plan to meet Bloomington’s power needs for thenext 20 years. The current capacity is 5000 kwh. The demand for the current year is 4000 kwh, and demand is expected to increase by 1000 kwh in each succeeding year. At the beginning of each year, Hoosier Power must determine the amount of capacity to add, given the following inputs: ■ Any year in which capacity is added, a fixed cost of $120,000 is incurred plus a cost of $120 per kwh of capacity. ■ At most 10,000 kwh of capacity can be added in a single year. ■ It costs $25 per year to maintain a unit of capacity. ■ It costs $12 per year to produce a kwh. ■ If production does not meet demand, a shortage cost of $80 per kwh short is incurred. Develop a linear integer model to help Hoosier Power minimize its costs for the next 20 years.arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning