Problema Solution
A boat builder determines that it costs $17,000 to manufacture 20 canoes in one month and $29,750 to manufacture 50 canoes in one month. Assuming that the relationship between cost and number of canoes produced is linear, find an equation that expresses this relationship.
Answer provided by our tutors
f(x) = m*x + b
where
x = the number of canoes produced
f(x) = the cost of x canoes produced
we need to find m and b
for x = 20 we have f(20) = 17,000
m*20 + b = 17000
for x = 50 we have f(50) = 29,750
m*50 + b = 29750
by solving the system of equations
m*20 + b = 17000
m*50 + b = 29750
we find
b = 8500
m = 425
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now we can write the expression
f(x) = 8500 + 425x