Class 2020.11.10

Clear[c,f]

eqn1=28*c+32*f==900

eqn2 = f==3*c

Solve[{eqn1,eqn2}, {f,c}]

N[%]

Solve[eqn1,f]

Plot[{3*c,(1/8) (225-7 c)},{c,0,33}, AxesLabel->{"c","f"}]

900.0/28

Problem #1 on HW 3.5 (press ALT+7 for a text cell, when done typing, simply go below the text cell to go back to mathematica input)

We have $30K to spend on municipal (M) and treasury (T) bonds.
advisor recommends that you invest twice as much in treasury as municipal

eqn3 = 30000== M+T
eqn4 = T==2*M

Solve[{eqn3,eqn4},{M ,T}]

Problem 4 on HW 3.5

Cost for brokerage firm is C, Revenue is R, T is transactions
$750/day to keep office open
brokers paid $25/transaction
fees collected: $35/transaction

Find a formula for C = C(T) => C = 25 *T + 750 
Find a formula for R = R(T) => R = 35*T

Clear[C]

eqn5 = C==25*T+750
eqn6 = R == 35*T

Find the # of transactions needed to make Revenue $1500 more than Cost.
R = C + 1500

(1500+750)/10

eqn7 = R==C+1500

Solve[{eqn5,eqn6,eqn7},{R, C, T}]

2250/10

eqn5

eqn6

eqn7

eqn7/.{R-> 35*T,C-> 750+25 T}

Solve[eqn7/.{R-> 35*T,C-> 750+25 T},T]