Number Theory
1) Find an integer that satisfies all three of the following:
1 mod 5 0 mod 2 4 mod 6
2) Encrypt the following message using sqrt(11) as the key (non repeating):
ENIGMAISBROKEN
3) Convert the following:
a. 2020 from base 10 to binary
b. 101110001 from binary to base 10
c. 1066 from base 10 to Hex
d. ABCD to from Hex to base 10
e. Bonus: A1B2C3D4 from Hex to binary
Financial Mathematics
4) Calculate your final balance after 5 years. You invest $1000 at 5.5% interest compounded semi-annually (twice a year).
5) Calculate your mortgage payment. You purchase a house for $200,000 and pay a 10% down payment. Your mortgage type and interest rate is a 30 year fixed rate mortgage at 3.750%.
6) You purchase a car for $10,000 and pay a $2,000 down payment. Your payment plan is for 3 years with 5% interest. How much is your monthly payment?
Linear Programming
7) A store sells two types of toys, A and B. The store owner pays $8 and $16 for each one unit of toy A and B respectively. One unit of toys A yields a profit of $3 while a unit of toys B yields a profit of $7. The store owner estimates that no more than 2000 toys will be sold every month and he does not plan to invest more than $20,000 in inventory of these toys. How many units of each type of toys should be stocked in order to maximize his monthly total profit profit?
a. Find the objective function and constraints. State whether a maximum/minimum is required.
b. Sketch the graph of the constraints. Label the feasible space and its vertices.
c. Solve for the possible min/max solutions of x,y
d. Determine the value of the objective function for each min/max and state the optimal solution.