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Emma Egli

Emma E.

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INSTANT ANSWER

Question 2. 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 \[ C_{M}(q)=\frac{1}{50} q^{3}+10000(\text { dollars) } \] to produce \( q \) widgets in a month, while in the Scarborough location it costs \[ C_{S}(q)=q^{2}+20000 \text { (dollars) } \] 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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Khoi V verified

Numerade educator

Question 2. 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 [ C_{M}(q)=frac{1}{50} q^{3}+10000( ext { dollars) } ] to produce ( q ) widgets in a month, while in the Scarborough location it costs [ C_{S}(q)=q^{2}+20000 ext { (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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The half-life of a certain element is 20 minutes. You weigh the element and record 80 grams. What is the instantaneous rate of change per minute 1.5 hours after your initial weighing?

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Derrick Danso verified

Numerade educator

A box of tissues cost $2.50 at the end of 2010. Assume prices go up 5% very year. What year will it be when the tissues cost $5.00?

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9. A passenger on a steamboat with a water wheel (see picture) notices an object that has become stuck on one of the paddles of the water wheel. She begins to keep track of its position above the water when it is at a point that is \( 7 \mathrm{~m} \) from the surface. The object then moved upwards to its highest point, \( 16 \mathrm{~m} \) above the surface of the water, then, \( 6 \mathrm{~s} \) later, to its lowest point \( 4 \mathrm{~m} \) below the surface of the water. [TIPS \( 3, A=1 \) ] a) Sketch a graph that represents the height of an object above the water, relative to the distance it has traveled for 2 rotations of the water wheel. Graph on the Separate Paper b) Determine an equation of the function, represented by this graph.

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INSTANT ANSWER

9. A passenger on a steamboat with a water wheel (see picture) notices an object that has become stuck on one of the paddles of the water wheel. She begins to keep track of its position above the water when it is at a point that is \( 7 \mathrm{~m} \) from the surface. The object then moved upwards to its highest point, \( 16 \mathrm{~m} \) above the surface of the water, then, \( 6 \mathrm{~s} \) later, to its lowest point \( 4 \mathrm{~m} \) below the surface of the water. [TIPS \( 3, A=1 \) ] a) Sketch a graph that represents the height of an object above the water, relative to the distance it has traveled for 2 rotations of the water wheel. Graph on the Separate Paper b) Determine an equation of the function, represented by this graph.

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