KidTOY uses three operations to assemble three types of toys- trains, trucks, and cars. The daily available times for the three operations are 430, 460, and 420 mins, respectively, and the revenues per unit of toy train, truck, and car are $3, $2, and $5, respectively. The assembly times per toy at each operation are shown in the table below.

Assembly times at the three operations (in minutes). (a zero time indicates that the operation is not used).

Toy Assembly #1 Assembly #2 Assembly #3

Train 1

Truck 2

Car 1

1

0

2

4

0

Letting x1, x2, and x, represent the daily number of units assembled of trains, trucks, and cars, respectively. The associated LP model is given as:

Maximize z = 3x, + 2x2 +5x3

subject to

Operation 1: x, +2x+ x 430

Operation 2: 3x,

+ 2x, 460

Operation 3: x,

+ 4x2 420

X1, X2, X3 20

The computer solution of the LP model is shown below.

a. Suppose that any additional time for operation 1 beyond its current capacity of 430 minutes per day must be done on an overtime basis at $50 an hour. Is it economically advantageous to use overtime with operation 1? Explain. (3 marks)

b. Suppose that the operator of operation 2 has agreed to work 2 hours of overtime daily at $55 an hour. What is the net effect of this activity on the daily revenue? Explain. (3 marks) c. Is overtime needed for operation 3? Explain. (2 marks)

d. Suppose that the daily availability of operation 1 is increased to 440 minutes and such overtime will cost $40 an hour. Determine the associated net revenue. (2 marks)

Maximize z=3x, + 2x2+5x3

subject to Operation 1: x, +2x+x, 430

Operation 2: 3x, +2x, 460

Operation 3: x, +4x, 5420

XXX, 20

The computer solution of the LP model is shown below.

a. Suppose that any additional time for operation 1 beyond its current capacity of 430 minutes per day must be done on an overtime basis at $50 an hour. Is it economically advantageous to use overtime with operation 1? Explain. (3) marks)

Suppose that the operator of operation 2 has agreed to work 2 hours of overtime daily at $55 an hour. What is the net effect of this activity on the daily revenue? Explain. (3 marks)

e. Is overtime needed for operation 3? Explain. (2 marks) d. Suppose that the daily availability of operation 1 is increased to 440 minutes and such overtime will cost $40 an hour. Determine the associated net revenue. (2 marks)

LP OPTIMUM FOUND AT STEP 2 OBJECTIVE FUNCTION VALUE

1)

1350.000

VARIABLE XI

VALUE 0.000000

REDUCED COST

4.000000

X2 100.000000 0.000000

X3

230.000000 0.000000

DUAL PRICES

CONSTRAINT SLACK OR SURPLUS

Operations I

0.000000 1.000000

Operations 2

0.000000

2.000000 Operations 3 20.000000 0.000000

NO. ITERATIONS

RANGES IN WHICH THE BASIS IS UNCHANGED:

OBJ COEFFICIENT RANGES

VARIABLE

CURRENT

ALLOWABLE INCREASE DECREASE

ALLOWABLE

COEF

XI

INFINITY

X2

2.000000

8.000000

2.000000

X3

5.000000 INFINITY 2.666667

CONSTRAINT

RIGHTHAND SIDE RANGES

CURRENT

ALLOWABLE

RHS

INCREASE

430.000000

10.000000

ALLOWABLE

DECREASE

200.000000

Operations I Operations 2

Operations 3

460.000000

20.000000

400.000000

INFINITY

20.000000