Question 1151909

 its MATHLOVER1. (• ◡•) ok 

large: {{{L}}} -> the manufacturing costs ${{{7}}}
 medium: {{{M}}}-> the manufacturing costs ${{{6}}}
small: {{{S}}}-> the manufacturing costs ${{{5}}}

cost: ${{{1390}}} for {{{250}}} statues:

{{{L+M+S=250}}}........eq.1
{{{7L+6M+5S=1390}}} ........eq.2
for revenue
{{{26L+18M+15S=4370}}} ........eq.3
-----------------------------------------------------solve the system

{{{L=250-M-S}}}........eq.1a
{{{L=1390/7-6M/7-5S/7}}} ........eq.2
----------------------------------------------- =>
{{{250-M-S=1390/7-6M/7-5S/7}}} 
{{{6M/7-M-S+5S/7=1390/7-250}}}......both sides multiply by {{{7}}}
{{{6M-7M-7S+5S=1390-1750}}}
{{{-M-2S=-360}}}.....solve for {{{M}}}
{{{M=360-2S}}}...............eq.1b

go to
{{{26L+18M+15S=4370}}} ........eq.3.............substitute {{{L}}} from eq.1 and {{{M}}} from eq.1b

{{{26(250-(360-2S)-S)+18(360-2S)+15S=4370}}} ............solve for {{{S}}}

{{{26(250-360+2S-S)+18(360-2S)+15S=4370}}}

{{{6500-9360+52S-26S+6480-36S+15S=4370}}}

{{{3620+5S=4370}}}

{{{5S=4370-3620}}}

{{{5S=750}}}

{{{S=750/5}}}

{{{highlight(S=150)}}}

go to {{{M=360-2S}}}...............eq.1a, substitute {{{S}}}

{{{M=360-2*150}}}

{{{M=360-300}}}

{{{highlight(M=60)}}}

go to {{{L=250-M-S}}}........eq.1a , substitute {{{S}}} and {{{M}}}

{{{L=250-60-150}}}

{{{L=250-210}}}

{{{highlight(L=40)}}}

answer: {{{highlight(L=40)}}}, {{{highlight(M=60)}}}, and {{{highlight(S=150)}}} should be made to produce ${{{4370}}} in monthly revenue


check:  If the number of statues above sell for ${{{26}}}, ${{{18}}}, and ${{{15}}}, respectively will  produce ${{{4370}}} in monthly revenue 

{{{4370=26L+18M+15S}}} 
{{{4370=26*40+18*60+15*150}}} 
{{{4370=1040+1080+2250}}} 
{{{4370=4370}}} which confirms our answer