Problem 1
In 2018, Shouldice Hospital admitted 14,800 patients. In 2019, a 20% increase in admissions is expected. Assume the hospital has 390 beds.
a) If the average patient stays in the hospital 8 days, how many beds were empty, on average, in 2018?
b) On average, how many beds do you expect to be empty in 2019?
Problem 2
A new vehicle leaves the assembly line at Cadillac’s plant every 55 seconds. Assume that at any moment, there are 800 vehicles on the line. How much time does it take for a vehicle to be assembled?
Problem 3
The total number of employees in a certain company remains constant. Due to turnover, on average, the company hires 150 men and 200 women each year. On average, a woman stays with the company 50% longer than a man does. What proportion of the total employees is women?
Problem 4
The Centurion apartment building in downtown Chicago has a total of 240 rental units. It offers its new tenants an 18-month lease, which is renewed on a month-to-month basis if the tenant chooses to stay longer than 18 months. The leasing office reports that The Centurion signs about 80 leases with new tenants in an average year, and that 60% of tenants who move in end up staying in the building longer than 18 months. On average, the building is 90% occupied. You may assume that a negligible number of tenants break their lease in the first 18 months.
a) What is the average number of tenants who are in their first 18 months at The Centurion?
b) What is the average length of stay (in months) for those tenants who stay longer than 18 months (counted from when they first sign their original lease)?
Problem 5
An insulation plant makes two types of insulation called type B and type R. Both types of insulation are produced using the same machine. The machine can produce any mix of output, as long as the total weight is no more than 70 tons per day. Insulation leaves the plant in trucks; the loading facilities can handle up to 30 trucks per day. One truckload of type B insulation weighs 1.4 tons; one truckload of type R weighs 2.8 tons. Each truck can carry type B insulation, type R insulation, or any mixture thereof. The insulation contains a flame retarding agent which is presently in short supply; the plant can obtain at most 65 canisters of the agent per day. One truckload of (finished) type B insulation requires an input of three canisters of the agent, but one truckload of type R insulation requires only one canister.
Carla Linton, the plant manager, has calculated that, at current prices, the contribution from each truckload of typ******** $********** $********for type R. There appears to be no difficulty in selling the entire output of the plant, no matter what production mix is selected. How much of each kind of insulation should be produced? Formulate the problem of determining the optimal number of truckloads of types B and R and use the Excel Solver to obtain a solution.
PLEASE USE EXCEL SOLVER APPLICATION FOR EACH ANSWER.