The cost of operating the Maintenance Department is to be allocated to four production departments based on the floor space each occupies. Department A occupies \( 900 \mathrm{~m}^{2} \); Department B, \( 800 \mathrm{~m}^{2} \); Department \( \mathrm{C}, 1200 \mathrm{~m}^{2} \); and Department \( \mathrm{D}, 500 \mathrm{~m}^{2} \). If the July cost was \( \$ 57,800 \), how much of the cost of operating the Maintenance Department should be allocated to each production department? The operating cost for Department A is \( \$ 15,300 \). (Simplify your answer.) The operating cost for Department B is \( \$ \) (Simplify your answer.)

To allocate the cost of operating the Maintenance Department, we first need to determine the total floor space occupied by all departments. Total floor space = \( 900 + 800 + 1200 + 500 = 3400 \, \mathrm{m}^2 \). Next, we can find the cost per square meter by dividing the total cost by the total floor space: Cost per square meter = \( \frac{\$ 57,800}{3400 \, \mathrm{m}^2} \approx \$ 17 \, \text{per} \, \mathrm{m}^2 \). Now we can allocate the costs based on each department's floor space: - For Department A: \( 900 \, \mathrm{m}^2 \times \$ 17 \, \approx \$ 15,300 \). - For Department B: \( 800 \, \mathrm{m}^2 \times \$ 17 \, \approx \$ 13,600 \). - For Department C: \( 1200 \, \mathrm{m}^2 \times \$ 17 \, \approx \$ 20,400 \). - For Department D: \( 500 \, \mathrm{m}^2 \times \$ 17 \, \approx \$ 8,500 \). So, the operating cost for Department B is \( \$ 13,600 \).