Final answer:
The correct expense function is not provided in the options. The demand function was rearranged to solve for price in terms of quantity, yielding an equation that does not match the listed options due to a quadratic term resulting from the multiplication of price by quantity.
Step-by-step explanation:
The given demand function is q = -300p + 10,000. To find the expense function in terms of q, we first need to express the price p in terms of q. Starting with the demand function, we add 300p to both sides and subtract q from both sides to get 300p = 10,000 - q. Then, we divide both sides by 300 to solve for p, yielding p = (10,000 - q) / 300. Multiplying both sides of this equation by q gives us the total expense, which is the price p times the quantity q. This gives us an expense function of E(q) = q × ((10,000 - q) / 300).
When we compute the equation, the term 10,000q/300 simplifies to 33.33q, and -q²/300 is subtracted from the expense. Since we're looking for an expense function in the form of E(q) = constant + coefficient × q, the options provided do not directly match our derived function. The options all add a constant to a product of q, but our function would have a quadratic term due to the -q²/300 component.
Therefore, the correct expense function is not listed among the options given. The closest in form is option d) 500,000 - 3.33q, but we deduced that there is an additional -q²/300 term in the actual function.