contestada

The Best Company produces two commercial products : blenders and mixers. Both products require a two step production process involving delivery of parts (JIT process) and assembly. It takes 1 hour to deliver parts for each blender and 2 hours for each mixer. Final assembly of mixers and blenders require 3 and 2 hours, respectively. The production capability is such that only 24 hours of delivery time and 30 hours of assembly time are available. Each blender produced nets the firm $7 and each mixer $6.

a) How many of each should be produced to maximize profit? Partial production of each product is allowed.
b) What is the $ amount of this profit?

Respuesta :

Answer:

Maximum profit is $87 when 3 blenders and 11 mixers are produced.

Step-by-step explanation:

let blender is represented by [tex]x_{1}[/tex] and and mixer by [tex]x_{2}[/tex].

total time to deliver parts = 24 hrs

total time to assemble = 30 hrs

time taken by each blender to deliver parts = 1 hr

time taken by each mixer to deliver parts = 2 hr

time taken by blenders in final assembling= 2 hr

time taken by mixers in final assembling = 3 hr

Each blender produced nets the firm=  $7

Each mixer produced nets the firm=  $6

Using this all data linear system of equation will be:

[tex]x_{1} + 2x_{2} =24  ----- (1)\\2x_{1} + 2x_{2} = 30 ----- (2)\\[/tex]

profit function:

[tex]z= 7x_{1} +6x_{2} --- (3)[/tex]

[tex]from (1)\\x_{1} = 0 \implies x_{2}= 12\\x_{2}= 0 \implies x_{1}= 24\\[/tex]

Coordinate points obtained from (1) are (0,12) and (24,0)

[tex]from (2)\\x_{1}=0 \implies x_{2}=10\\x_{2}=0 \implies x_{1}=15\\[/tex]

Coordinate points obtained from (2) are (0,10) and (15,0)

plotting these on graph

points lying in feasible region are:

A(0,0)

B(0,10)

C(3,11)

D(12,0)

substituting these points in (3) to find the maximum profit:

for A (0,0)

z = 0

for B (0,10)

z = 60

for C (3,11)

z =  87

for D (12,0)

z=84

So maximum profit is $87 when 3 blenders and 11 mixers are produced.

Otras preguntas