Management Science
Midterm Examination
II. Word Problems. Solve the following problems correctly as you can. Show
your solutions. Submit answer to my email add ruben.sanchez@pcu.edu.ph
1. Using Gaussian Elimination
a. x – y – 2z = 7
b.
6x + 4y – z = 3
2x – 3y + 2z = 0
x + 2y + 4z = -2
X – 2y – 3z = 3
5x + 4y – 2z = 0
2. By any method
a. 7x – y = 9
x + 3y + 2z = -1
7x – 1 = y
2x + 3y + 3z = -2
-2x + 2y – 3z = 7
3. IJC Electronics assembles stereo equipment, VCD players and cassette players.
The company makes a profit of P200 on each VCD player and P120 on each cassette
player. Both must go through two steps – assembly and quality control. A VCD
player takes 12 hours to assemble and 5 hours to bench check. A cassette player
takes 4 hours to assemble but 8 hours to bench check. The company has 60
assembly hours uncommitted and 40 hours of checking time available. Use the
graphical method to find best combinations of VCD and cassette players.
4. JRC Products, Inc. produces two brands of cat food called Kitty - C and Kitty-D.
Contributions from Kitty-C is P50 per pack while Kitty-D yields a contribution of P60 per
pack. Both products are blended from two basic ingredients - a protein source and a
carbohydrate source products require the following ingredients:
Protein Carbohydrates
Kitty-C 4 kg.
3 kg.
Kitty-D 2 kg.
1 kg.
For the week only 700 kg of protein source and 500 kg. of carbohydrate source are
available. How many bags of each of the two brands should be produced to maximize
profit?
5. Three kilograms of peanut and 8 kilograms of cornbits costs P397 and 5 kilograms
of peanut and 6 kilograms of cornbits costs P471. What is the cost per kilogram of
peanut, and what is the cost per kilogram of cornbits?
6. MJ Santos placed an investment that yields an annual interest of P7500. If P5000
more is invested and the rate is 1 percent less, the annual interest is P6500. What
is the amount of the investment and the rate of interest?
Good Luck Everyone and Advance Merry Christmas
Dr. Ruben A. Sanchez