A standard piano has 88 keys on it
Step-by-step explanation:
let us give all the quantities in the problem variable names.
x= amount in utility stock
y = amount in electronics stock
c = amount in bond
“The total amount of $200,000 need not be fully invested at any one time.”
becomes
x + y + c ≤ 200, 000,
Also
“The amount invested in the stocks cannot be more than half the total amount invested”
a + b ≤1/2 (total amount invested),
=1/2(x + y + c).
(x+y-c)/2≤0
“The amount invested in the utility stock cannot exceed $40,000”
a ≤ 40, 000
“The amount invested in the bond must be at least $70,000”
c ≥ 70, 000
Putting this all together, our linear optimization problem is:
Maximize z = 1.09x + 1.04y + 1.05c
subject to
x+ y+ c ≤ 200, 000
x/2 +y/2 -c/2 ≤ 0
≤ 40, 000,
c ≥ 70, 000
a ≥ 0, b ≥ 0, c ≥ 0.
Answer:
parallelogram
Step-by-step explanation:
slope of DE = (4-7) / (-4 - 2) = 1/2
slope of FT = (-3 - -6) / (11-5) = 1/2
DE // FT
slope of EF = (-6 - 4) / (5 - -4) = - 10/9
slope of DT = (-3 - 7) / (11 - 2) = - 10/9
EF // DT
Answer:
the slope is 0, 2, 4, 6, 8 , and 10
Step-by-step explanation:
