Layton Machining Company (LMC) manufactures two versions of a basic machine tool. One version is a standard model and one is a custom model, which requires some additional work and slightly higher-grade materials. The manufacturing process at LMC requires that each product go through two departments, Grinding and Finishing. The process in each department uses a single type of machine. Total machine capacity in Grinding is 51,000 hours, and in Finishing, total machine capacity is 31,000 hours. (Each department has multiple machines.) Total market demand is limited to 102,000 standard units and 122,000 custom units monthly. LMC is currently producing 92,000 standard units and 53,000 custom units each month. Cost and machine-usage data for the two products follow:

a. What is the optimal production schedule for LMC? In other words, how many standard units and custom units should the company produce each month to maximize monthly profit?

Standard Units ____

Custom Units ____

b. If LMC produces at the level found in requirement (a), how much will monthly profit increase over the current production schedule?

Increase profits by ____

CODE: C#
using System;
public static class Lab6
{
   public static void Main()
   {
      // declare variables
      int hrsWrked;
      double ratePay, taxRate, grossPay, netPay=0;
      string lastName;

     // enter the employee's last name
     Console.Write("Enter the last name of the employee => ");
     lastName = Console.ReadLine();

     // enter (and validate) the number of hours worked (positive number)
     do
     {
        Console.Write("Enter the number of hours worked (> 0) => ");
        hrsWrked = Convert.ToInt32(Console.ReadLine());
     } while (hrsWrked < 0);

     // enter (and validate) the hourly rate of pay (positive number)
     // *** Insert the code to enter and validate the ratePay

     // enter (and validate) the percentage of tax (between 0 and 1)
     // *** Insert the code to enter and validate taxRate

     // Call a method to calculate the gross pay (call by value)
     grossPay = CalculateGross(hrsWrked, ratePay);

     // Invoke a method to calculate the net pay (call by reference)
     CalculateNet(grossPay, taxRate , ref netPay);

     // print out the results
     Console.WriteLine("{0} worked {1} hours at {2:C} per hour", lastName,
                       hrsWrked, ratePay);
     // *** Insert the code to print out the Gross Pay and Net Pay
     Console.ReadLine();
  }

  // Method: CalculateGross
  // Parameters
  //      hours: integer storing the number of hours of work
  //      rate: double storing the hourly rate
  // Returns: double storing the computed gross pay
  public static double CalculateGross(int hours, double rate)
  {
     // *** Insert the contents of the CalculateGross Method
  }

  // Method: CalculateNet
  // Parameters
  //      grossP: double storing the grossPay
  //      tax: double storing tax percentage to be removed from gross pay
  //      netP: call by reference double storing the computed net pay
  // Returns: void
  public static void CalculateNet(double grossP, double tax, ref double netP)
  {
     // *** Insert the details of the CalculateNet Method
  }
}

1. Build the solution. Resolve any syntax mistakes (if you make any) until the program compiles. Run the program using the input data: Smith, 40, 12.5, 0.2. You should find that the gross pay is $500.00 and net pay is $400.00

   What is the output?

2. Run the program using input Smith, -8,40, 12.5, 0.2.

   What is the output?

3. Run the program using input Smith, 40,-3, 12.5, 0.2.

   What is the output?

4. Run the program using input Smith, 40,12.5, 9, 0.2.

   What is the output?

5. Run the program using input Smith, 44,12.5, 0.2.

   What is the output?

6. Now let’s add another user-defined method to our program ... this method will compute any overtime pay.

   Assume the employees receive time and a half (1.5) for any hours worked over 40).

   Your method should be invoked after you compute gross pay with CalculateGross but before you compute net pay with CalculateNet (i.e., between Lines 36 and 39).

   The new method is to be called CalculateOT, and it is to have to following method header:

   public static double CalculateOT(int hours, double rate)

   In this method, both formal parameters are call by value with hours representing the number of hours work and rate representing the hourly wage.

   CalculateOT is to return only the amount of overtime pay (in excess of regular pay) which is computed from the number of hours greater than 40 multiplied by the hourly wage and then multiplied by 0.5. (CalculateOT is only returning the overtime amount which must be added to the gross pay variable in Main() before netPay is calculated )    Run the program using the input data: Smith, 40, 12.5, 0.2.

7. Run the program using input Smith, 44,12.5, 0.2. (The grossPay for this data should be $575 and the netPay should be $460. If you get a different answer, you've made a mistake and should revisit your code.)

8. What is the output?

   How does the result differ from Part (f)?

9. Run the program using input Smith, 20,12.5, 0.2.

   The grossPay for this data should be $250 and the netPay should be $200. If you get a different answer, you've made a mistake and should revisit your code.

   What is the output?

If your bank account pays annual interest rate of 0.2% and compounds the interest every day, how much is the future value of $500 saved in the account for 3 years? (include the equation)

Hint: Assume there are 365 days per year.

Biochemistry: Enzyme Units

Can relative activity be added together? For example, if fraction A has 0.2 U/mL and fraction B has 0.4 U/mL, will combining the two fractions produce a solution with a relative activity of 0.6 U/mL?

2) A solid sphere with mass 2kg and radius 0.2 meters is rotating clockwise about its center with ωi =5 rad/s. a) Find its Moment of Inertia. b) We want to double its angular speed in 3 full turns of the sphere. Find its acceleration. c) A constant force is acting on the edge with 135 degrees angle. Find the Force needed to for this acceleration

1) A stone with mass 240 g is swirled around using a 0.2 m long rope such that it makes 10 full revolutions in 17 seconds. a) The speed of the stone is v = m/s. b) The tension in the rope is T = N. c) Work done by the tension force is W = J.

2) A puck is kicked up an icy incline with an initial speed of 3.4 m/s. The angle of the incline is 31 °. The kinetic coefficient of friction of the puck on ice is μ = 0.15.
a) The time it take for the puck to go up and come back down is t =  s.
b) The maximum distance traveled by the puck up the incline until is d =  m.
c) Find the maximum elevation the puck goes up the incline by using the principle of conservation of energy. The height h =  m.

3) The electricity price is 10 cents per kWh. What is the monthly cost of electricity for running a light bulb that consumes 70 J per second for 6 hours per day? The cost is $ ___

4) The work done by a force given by  = 2 x³  + 7 y²  N that acts on an object that moves along the y axis from y_i = 4 m to y_f = 6 m is  J.

Let x be an exponential random variable with lambda equals 0.2. Calculate the probabilities described below.

a. ​P(x<7​)

b. ​P(x>8​)

c. ​P(7< = x < = 8​)

d. ​P(x> = 6​)

e. the probability that x is at most 8

5. How many grams of solid NaCNO must be added to 100 mL of 0.2 M HCNO at 25°C to obtain a buffer at pH = 4.00?

13. What is the pH of the buffer formed when 200 mL of 0.04 M propionic acid is mixed with 50 mL of 0.12 M sodium propionate (NaC₃H₅O₂)at 25 °C?

You add 300 mL of Tris-HCl at 0.1 M to a 0.2 L solution of 0.9% (w/v)NaCl, and to which you add 500 mg of NaCl (powder).
What is the concentration of Tris-HCl in mM and in g/L?
Tris-HCl : MW 121.14
NaCl : MW 58.44

Consider a binomial experiment with n=.14 with and p= 0.2.

a. Compute F(0) (to 4 decimals).

b. Compute f(12) (to 4 decimals).

c. Compute P(x< or equal to 1) (to 4 decimals).

d. Compute P(x >or equal to 4) (to 4 decimals).

e. Compute E(x) (to 1 decimal).

f. Compute Var(x) and mean . (to 2 decimals) (to 2 decimals)