In class we derived a differential equation that governs the spatial temperature distribution inside a fin with uniform cross-sectional area that is exposed to convection. Beginning with a differential control volume, derive a differential equation that governs the spatial temperature distribution inside a fin with uniform cross-sectional area that is exposed to both convection (with T. and h) and a uniform radiation heat flux arad. Assume conduction inside the fin is 1- D, steady state, constant properties, no heat generation inside the fin, that the base temperature of the fin To is higher than T., and grad is into the fin.

Zachary company produces commercial gardening equipment. since production is highly automated, the company allocates its overhead costs to product lines using activity-based costing. the costs and cost drivers associated with the four overhead activity cost pools follow: activities unit level batch level product level facility level cost $ 64,800 $ 27,730 $ 15,000 $ 154,000 cost driver 2,400 labor hrs. 47 setups percentage of use 11,000 units production of 780 sets of cutting shears, one of the company’s 20 products, took 240 labor hours and 7 setups and consumed 15 percent of the product-sustaining activities. required: (a) had the company used labor hours as a company wide allocation base, how much overhead would it have allocated to the cutting shears? (b) how much overhead is allocated to the cutting shears using activity-based costing? (c) compute the overhead cost per unit for cutting shears first using activity-based costing and then using direct labor hours for allocation if 780 units are produced. if direct product costs are $150 and the product is priced at 30 percent above cost for what price would the product sell under each allocation system? (d) assuming that activity-based costing provides a more accurate estimate of cost, indicate whether the cutting shears would be over- or underpriced if direct labor hours are used as an allocation base. explain how over-or undercosting can affect vaulker's profitability. (e) comment on the validity of using the allocated facility-level cost in the pricing decision. should other costs be considered in a cost- plus pricing decision? if so, which ones? what costs would you include if you were trying to decide whether to accept a special order?