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MyCollege Clothing Company manufactures expensive sweatshirts to sell to college bookstores in orders of up to 75. MyCollege Clothing has created a cost function to make x number of sweatshirts... C(x) = 4000 + 0.25x? 0sxs75 MyCollege Clothing finds that in order to sell x sweatshirts, the price per shirt must be p = 150 - 0.5x. A) Graph the cost function. (Be sure to include all key information in the graph.) B) What are MyClothing's fixed costs? Where can these be seen in the graph? C) Find the revenue function and graph it on the same axes as the cost function. (Be sure to include all key information in the graph.)

MyCollege Clothing Company manufactures expensive sweatshirts to sell to college bookstores in orders of up to 75. MyCollege Clothing has created a cost function to make x number of sweatshirts... C(x) = 4000 + 0.25x? 0sxs75 MyCollege Clothing finds that in order to sell x sweatshirts, the price per shirt must be p = 150 - 0.5x. A) Graph the cost function. (Be sure to include all key information in the graph.) B) What are MyClothing's fixed costs? Where can these be seen in the graph? C) Find the revenue function and graph it on the same axes as the cost function. (Be sure to include all key information in the graph.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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MyCollege Clothing Company manufactures expensive sweatshirts to sell to college bookstores in orders of up to 75. MyCollege Clothing has created a cost function to make x number of sweatshirts.. C(x) = 4000 + 0.25x² 0sxs75 MyCollege Clothing finds that in order to sell x sweatshirts, the price per shirt must be p = 150 - 0.5x. A) Graph the cost function. (Be sure to include all key information in the graph.) B) What are MyClothing's fixed costs? Where can these be seen in the graph? C) Find the revenue function and graph it on the same axes as the cost function. (Be sure to include all key information in the graph.) D) What is the point(s) of intersection of these two graphs? (Be sure to give and x and y coordinate.) E) What does the intersection of these two graphs mean in the context of the problem? F) Find the profit function. Graph the profit function in a new set of axes. (Be sure to include all key information in the graph.) G) How many sweatshirts should MyCollege Clothing manufacture to make a profit? Where can I find this in the profit function created in F? (Round your answer up to the nearest whole number.) H) The lona College intern suggests that the company should increase the number of sweatshirts it will sell in an order, because they are not maximizing their profits for each order. H1) Find the marginal profit. H2) How does the marginal profit show that the company can continue to increase its profit? H3) What number of sweatshirts should they make and sell to maximize the profits? H4) What would the maximum profit be?
Transcribed Image Text:MyCollege Clothing Company manufactures expensive sweatshirts to sell to college bookstores in orders of up to 75. MyCollege Clothing has created a cost function to make x number of sweatshirts.. C(x) = 4000 + 0.25x² 0sxs75 MyCollege Clothing finds that in order to sell x sweatshirts, the price per shirt must be p = 150 - 0.5x. A) Graph the cost function. (Be sure to include all key information in the graph.) B) What are MyClothing's fixed costs? Where can these be seen in the graph? C) Find the revenue function and graph it on the same axes as the cost function. (Be sure to include all key information in the graph.) D) What is the point(s) of intersection of these two graphs? (Be sure to give and x and y coordinate.) E) What does the intersection of these two graphs mean in the context of the problem? F) Find the profit function. Graph the profit function in a new set of axes. (Be sure to include all key information in the graph.) G) How many sweatshirts should MyCollege Clothing manufacture to make a profit? Where can I find this in the profit function created in F? (Round your answer up to the nearest whole number.) H) The lona College intern suggests that the company should increase the number of sweatshirts it will sell in an order, because they are not maximizing their profits for each order. H1) Find the marginal profit. H2) How does the marginal profit show that the company can continue to increase its profit? H3) What number of sweatshirts should they make and sell to maximize the profits? H4) What would the maximum profit be?
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