1. The problem asks to find the 2000 purchased cost of similar shell-and-tube heat exchangers with different heating surfaces, starting from a 1990 cost of $4200 for 100 m^2. 2. The chemical engineering plant cost index is applied to update the cost from 1990 to 2000. 3. The capacity cost estimation formula is: $$C_2 = C_1 \times \left(\frac{A_2}{A_1}\right)^n \times \frac{I_2}{I_1}$$ where: - $C_1 = 4200$ is cost in 1990 for 100 m^2 - $A_1 = 100$ m^2 - $A_2$ is new heating surface area (given for parts c and d) - $n$ is the capacity exponent - $I_1$ is cost index for 1990 - $I_2$ is cost index for 2000 4. From Chemical Engineering Plant Cost Index, the approximate values: - $I_{1990} = 370.2$ - $I_{2000} = 459.2$ ### Part c: 30 m^2 heating surface, $n=0.6$ (surface range 10-40 m^2) $$C_2 = 4200 \times \left(\frac{30}{100}\right)^{0.6} \times \frac{459.2}{370.2}$$ Calculate: 1. $\left(\frac{30}{100}\right)^{0.6} = (0.3)^{0.6} \approx 0.4857$ 2. Cost index ratio: $\frac{459.2}{370.2} \approx 1.2406$ 3. So, $$C_2 = 4200 \times 0.4857 \times 1.2406 \approx 4200 \times 0.6026 = 2530.9$$ ### Part d: 175 m^2 heating surface, $n=0.81$ (surface range 40-200 m^2) $$C_2 = 4200 \times \left(\frac{175}{100}\right)^{0.81} \times \frac{459.2}{370.2}$$ Calculate: 1. $\left(\frac{175}{100}\right)^{0.81} = (1.75)^{0.81} \approx 1.6158$ 2. Cost index ratio: $1.2406$ (same as above) 3. So, $$C_2 = 4200 \times 1.6158 \times 1.2406 \approx 4200 \times 2.004 \approx 8416.8$$ ### Part 2: Total capital investment in 2000 The problem states “total capital investment needed from problem 1 in 2000”. Assuming this means summing costs for both sizes: $$Total = 2530.9 + 8416.8 = 10947.7$$ **Final answers:** 1. c) New cost for 30 m^2 heating surface in 2000 is approximately $2531$ 2. d) New cost for 175 m^2 heating surface in 2000 is approximately $8417$ 3. Total capital investment needed for both in 2000 is approximately $10948$