City and Country Cycles sells two kinds of bicycles mountain

City and Country Cycles sells two kinds of bicycles, mountain bikes and racing bikes. They have $63,000 to spend on new bikes and 390 hours of assembly time to put them together. Each mountain bike costs $300 wholesale and takes two hours to assemble. Each racing bike costs $420 wholesale and takes two-and-one-half hours to assemble. How many of each can the shop buy and assemble to use all available money and time?

Solution

this is a linear optimization question.

we have to maximize the number of bicycles produced

let b₁ and b₂ be the mountain bike abd racing bike respectively

since

they have total amount to spend=$63000

they have total time to assemble=390 hours

then according to question we have to find the maximum of (b₁+b₂)

now let us form the equation (from question given)

2b₁+2.5b₂=390......................(1)

$300b₁+$420b₂=$63000

$30b₁+$42b₂=$6300..............(2)

multipling (1) by 2 and substracting it from equation ( 2)

b₂=100

b₁=70

therefore maximum=100+70=170