Use graphical methods to solve each linear programming problem. Q7. Alfred Juare

Question

Use graphical methods to solve each linear programming problem. Q7. Alfred Juarez owns a small publishing house specializing in Latin American poetry. His fixed cost to produce a typical poetry volume is $525, and his total cost to produce 1000 copies of the book is $2,675. His books sell for $4.95 each. (a) Find the linear cost function for Alfred's boolk productiorn. b) How many poetry books must he produce and sell in order to break even? o) How many books must he produce and sell to make a profit of $1000?

Explanation / Answer

a) linear cost function is

( 0 , 525 ) and ( 1000, 2675 )

m = 2.15

linear function becomes

C(x) = 2.15 x + 525

where x is the number of copies

sell function is

S(x) = 4.95 x

b) breakeven occurs when cost function is equal to sell function

2.15 x + 525 = 4.95x

x = 188

so , he must sell 188 books in order to break even

c) profit function is

P(x) = 2.80x - 525

1000 = 2.80x - 525

x = 545

so, he must produce and sell 545 books to make a profit of $ 1000

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