Hartman Company is trying to determine how much of each of two products should be produced over the coming planning period. The only serious constraints involve labor availability in three departments. Shown below is information concerning labor availability, labor utilization, overtime, and product profitability.

If all production is done in a standard workweek, then Profit per Unit includes the cost to pay for the workforce. But, if overtime is needed in each department, then the Profit Function needs to be reduced by the Cost per Hour of Overtime in Each Department multiplied by the Number of Overtime Hours Used in Each Department. For example, if we used 5 hours of Overtime in Department A, we would need to Subtract $22*5 from our Profit equation.


Setup and Solve the Linear Programming Problem and determine the number of units of Product 1 and Product 2 to produce to Maximize Profit. Add an Additional Constraint to your LP to make sure that ALL of the Variables are INTEGERS


Hint: You will need 5 Decision Variables, 2 of them to determine the production quantities, and 3 of them to determine how much overtime to use in each of the departments.

Max Profit = $

(Do Not Use Commas) Hint: Max Profit is Between $3169 and $3569
Number of Units of Product 1 to Produce =

Number of Units of Product 2 to Produce =

Overtime in Department A =

Overtime in Department B =

Overtime in Department C =

(hours)

1. The market and Stock J have the following probability distributions.  Calculate the standard deviations for the Stock J.

   Probability	r M	r J
   0.3	-10%	10%
   0.4	20%	18%
   0.3	25%	30%

   		6.22%
   		14.87%
   		12.50%
   		3.85%
   		7.81%

The sample proportion p-bar provides an estimate for the population proportion p. The sampling distribution of the sample proportion is the probability distribution of the sample proportion.

Consider a population with a proportion p = 0.60, from which a sample of size n = 200 is drawn. What is the sampling distribution of the sample proportion p-bar?

Calculate the following probabilities using the distribution above:

P(? < 0.5)

P(? > 0.7)

P(0.5 < ? < 0.7)

In a non-ideal Rankine cycle saturated vapor (x=1) enters the turbine at 8.0 MPa and saturated liquid water (x=0) exits the condenser at a pressure of Pexit. Pexit = 0.006 MPa. The net power output of the cycle is given as 100 MW. Knowing that the isentropic efficiency of the pump is 0.85 generate the following plots in Excel or in similar programs for the given range of the isentropic efficiency of the turbine. (Please submit your Excel sheet or your computer program with the homework.)

a) Isentropic efficiency of the turbine 0.7 < ?T < 0.9 vs. steam mass flow rate

b) Isentropic efficiency of the turbine 0.7 < ?T < 0.9 vs. Rate of heat transfer from the boiler to the compressed water at the outlet of the pump

c) Isentropic efficiency of the turbine 0.7 < ?T < 0.9 vs. thermal efficiency of the cycle

Identifyassumptions you need to make to prepare financial forecasts.

Discuss the risk of leasing hotel rooms to investors.

Which of the solutions below is hyperosmotic, isoosmotic, and hypoosmotic relative to the Red Blood Cells (RBCs) BEFORE and AFTER blood is added?

0.15 M Urea

Before:

After:

What is the osmolarity before and after blood is added?

0.3 M NaCl + 0.3 M Urea

Daily sales at a store is a random variable, with values of $100, 300, 500, and 800 with probabilities 0.2, 0.2, 0.5, and 0.1 respectively. What is the expected value of sales?

Suppose the economy of a large nation has a defense industry, a banking industry, and a pharmaceutical industry. 1-unit output of defense requires 0.6 inputs of defense, 0.2 inputs of banking, and 0.2 inputs of pharmaceuticals. 1-unit output of banking requires 0.1 inputs of defense, 0.4 inputs of banking, and 0.5 inputs of pharmaceuticals. 1-unit output of pharmaceuticals requires 0.1 inputs of defense, 0.2 inputs of banking, and 0.2 inputs of pharmaceuticals.

If the nation wants to have surpluses of 106 units of defense production, 243 units of banking production, and 216 units of pharmaceutical production, find the gross production of each industry.

For the amusement of the guests, some hotels have elevators on the outside of the building. One such hotel is 300 feet high. You are standing by a window 100 feet above the ground and 150 feet away from the hotel, and the elevator descends at a constant speed of 30 ft/sec, starting at time

t = 0,

where t is time in seconds. Let θ be the angle between the line of your horizon and your line of sight to the elevator.

(a) Find a formula for

h(t),

the elevator's height above the ground as it descends from the top of the hotel.
h(t) =  

  

(b) Using your answer to part (a), express θ as a function of time

t.

θ(t) =  

tan−1(2−t5​)

Find the rate of change of θ with respect to t.

=  

(c) The rate of change of θ is a measure of how fast the elevator appears to you to be moving. At what height is the elevator when it appears to be moving fastest?
h =