Consider the price-demand equation and cost function p = 217 - 8x C(x) =79+ 68x- 3x2 for 0

Consider the price-demand equation and cost function p = 217 8x C(x) = 79 + 68x 3x2 for 0 s x s 100. la. Determine the.value of x and the corresponding price that maximizes the profit. items dollars price: 1b. If the government imposes a tax on the company of $23 per unit quantity produced, determine the new price that maximizes the profit. dollars price: lc. [WRITTEN PROBLEM] Using full sentences, answer the following question: Is it in the company's best interest to respond to the $23 tax by raising the price of the item by $23? Use your answers above to explain why or why not. 2. Suppose the government imposes a tax of T dollars per unit quantity produced (where 0 T 148. The new cost function is C(x) =79+68x-3x2 + Tx, o S x s 100 original cost a. Determine the new value of X that maximizes the company's profit and write as a function of T. items b. Assuming that the company cuts back production to this level, express the tax revenues received by the government as a function of T. Determine the value of T that will maximize the tax revenue received by the government. Taxes: dollars 3, [WRITTEN PROBLEM) In this case study, the location of the maximum of a quantity was computed several times. Include the justification (i.e. why rnax?) for at least one of the calculations above,