Strathmore Institute of Mathematical Sciences
BBSc. Financial Engineering
Assignment
BSM 3220 - Optimization Methods in Finance
Due date: F riday, 11th N ovember 2022
Instructions
ˆ NO SUBMISSIONS BY EMAIL.
ˆ Submit hardcopies of your work to me by the indicated date.
1. Use graphical method to maximize T = 3b + 4a subject to a + 2b ≤ 30,
3a + b ≤ 45, a, b ≥ 0
[5 Marks]
2. Casio Electricals Ltd. produces two types of light emitting diodes
(LED) for their CASIO calculators P and Q. Diodes are produced
and sold on a weekly basis. The weekly production cannot exceed 25
for diode P and 35 for diode Q because of limited available facilities.
The company employs total of sixty workers. Diode P requires 2 manweeks of labour, while diode Q requires one man-week of labour. Profit
margin on diode P is 60K.Sh and on diode Q is 40K.Sh. Formulate
this problem as an LP problem and solve it using graphical method.
.
[7 Marks]
3. Reynold, a carpenter makes two types of furniture: lazy-boy and sofas.
The production of the sofas and lazy-boys requires three operations –
carpentry, finishing, and upholstery. Manufacturing a lazy-boy requires
3 hours of carpentry, 9 hours of finishing, and 2 hours of upholstery.
Manufacturing a sofa requires 2 hours of carpentry, 4 hours of finishing,
and 10 hours of upholstery. The factory has allocated at most 66 labour
hours for carpentry, 180 labour hours for finishing, and 200 labour hours
1
for upholstery. The profit per lazy-boy is K.Sh.90 and the profit per
sofa is K.Sh.75. How many lazy-boys and how many sofas should be
produced each day to maximize the profit? (Use Simplex method).
.
[8 Marks]
4. Given the LPP Max Z = a+2b+c such that 2a+b−c ≤ 2, 4a+b+c ≤ 6,
a, b, c ≥ 0. Solve both the primal and the dual using simplex method
and compare your answers.
.
[14 Marks]
5. A tailor makes two types of hooded jumpers. Type one needs 200gm
of corespun thread, 300gm of some denim thread and 300gm of lanon
thread. The second type needs 200gm of corespun, 200gm od denim
and 100gm of lanon threads. He makes a profit of K.Sh.19.50 on type
one and K.Sh.15.90 on the second. In store, he has 24kg of corespun,
26kg of denim and 22Kg of lanon threads. Help him maximize his
profit and explain how the duality concept can be used to determine
the right prices for various kinds of threads.
[10 Marks]
6. Given the quadratic programming problem (QPP):
M inimize : P (q, r) = 0.5q 2 + 0.5r2
s.t, 2q − r − 5 = 0
2
[6 Marks]