Company XYZ produces and sells widgets. Production is done at two separate factories, one in Mississauga and one in Scarborough. An analysis reveals that in the Mississauga location, it costs CM (q) = 1 q3 + 10000 (dollars) 50 to produce q widgets in a month, while in the Scarborough location it costs CS (q) = q2 + 20000 (dollars) to produce q widgets in a month. The company needs to fulfill orders for a total of 400 widgets in the month of March 2023. (a) How many widgets should each location be assigned to produce so that the total cost of production is minimized? (b) Due to differences in quality control and shipping costs, company XYZ decides to sell widgets produced at each factory at different price levels: widgets produced in Mississauga are to be sold for $2000 each, and widgets produced in Scarborough for $2800 each. Show that it is most profitable for the company to allocate all production to Scarborough.
Company XYZ produces and sells widgets. Production is done at two separate factories, one in Mississauga and one in Scarborough. An analysis reveals that in the Mississauga location, it costs
CM (q) = 1 q3 + 10000 (dollars) 50 to produce q widgets in a month, while in the Scarborough location it costs
CS (q) = q2 + 20000 (dollars) to produce q widgets in a month.
The company needs to fulfill orders for a total of 400 widgets in the month of March 2023.
(a) How many widgets should each location be assigned to produce so that the total cost of production is minimized? (b) Due to differences in quality control and shipping costs, company XYZ decides to sell widgets produced at each factory at different price levels: widgets produced in Mississauga are to be sold for $2000 each, and widgets produced in Scarborough for $2800 each. Show that it is most profitable for the company to allocate all production to Scarborough.
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