(Solved): A manufacturer of handcrafted wine racks has determined that the cost to produce x units pe month i ...

A manufacturer of handcrafted wine racks has determined that the cost to produce $\mathrm{x}$ units pe month is given by $\mathrm{C}=0.3{\mathrm{x}}^2+10,000$. How fast is the cost per month changing when production is changing at the rate of 19 units per month and the production level is 70 units? Costs are at the rate of $\$$ per month at this production level. (Round to the nearest dollar as needed.) The price $\mathrm{p}$ (in dollars) and demand $\mathrm{x}$ for wireless headphones are related by $x=7,000?0.15p^2$. The current price of $\$100$ is decreasing at a rate $\$5$ per week. Find the associated revenue function $R(p)$ and the rate of change (in dollars per week) of revenue. $R(p)=$ $\frac{d}{dt}(R(p))=$ The rate of change of revenue is dollars per week. (Simplify your answer. Round to the nearest dollar per week as needed.)