A farmer sells organic apples at a local market. The fixed costs are $800 per season, and the variable cost is $1 per kilogram of apples sold. The revenue is $0 when 0 kg or 160 kg of apples are sold due to market limitations. The maximum revenue occurs when 80 kg of apples are sold. Which system of equations represents the linear cost function C(x) and the quadratic revenue function R(x) , where x represents the kilograms of apples sold?
Answer
A
cap c times x is equal to x plus 800 cap r times x is equal to negative x times open paren x minus 80 close paren
B
cap c times x is equal to x plus 800 cap r times x is equal to negative x times open paren x minus 160 close paren
C
cap c times x is equal to 800 x plus 1 cap r times x is equal to negative x times open paren x minus 160 close paren
D
cap c times x is equal to 800 x plus 1 cap r times x is equal to negative x times open paren x minus 80 close paren
Explanation
The cost function is fixed cost plus variable cost per kilogram: C(x) = 800 + 1x. Revenue is zero at x = 0 and x = 160, so its factors must be x and (x − 160). Since revenue reaches a maximum between those zeros, the parabola opens downward, giving R(x) = −x(x − 160). Thus the system in choice B is correct.
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