ABC Health Product Company is embarking on a $6$-year plan for the production and sale of a new he

Question

ABC Health Product Company is embarking on a $6$-year plan for the production and sale of a new health product for young adults. Mr Lim, the company’s finance manager, models the cost of production, $C$ thousand dollars per year, at time $t$ years into the plan using the equation $C=t^3-9t^2+15t+55$, for $0 \le t \le 6$. Use differentiation to find the values of $t$ which give stationary points on the graph of $C$ against $t$. For each point, justify whether it is a maximum or minimum.[5] Sketch the graph of $C$ against $t$, giving the coordinates of the end points and any intersections with the axes.[2] Mr Lim also projects the revenue from sales of the new health product, $R$ thousand dollars per year, at time $t$ years using the equation $R=36\ln(t+1)$, for $0 \le t \le 6$. Sketch the graph of $R$ against $t$ for $0 \le t \le 6$, indicating the coordinates of the end points.[1] Find the value of $\displaystyle\int\nolimits_0^6 36\ln(t+1) \, \mathrm{d}t$, correct to $3$ decimal places and provide an interpretation of this value in the context of the question.[2] Hence, determine with reason whether the company should embark on this $6$-year plan for the new health product.[2]

Accepted Answer

(i)(1,61), maximum and (5,30), minimum (iv)274.369

2024 RVHS H1 Q5

2024 RVHS H1 Q5