A company manufactures two ypes o wood-burning stoves: a reestanding model and a

Question

A company manufactures two ypes o wood-burning stoves: a reestanding model and a insert stoves is replace insert model The cost fun on or rod cin ·reestandin and replace- C-32Vxy+ 185x +220y1050 (a) Find the marginal costs (ac/ax and ac/ay) when x-80 and y 20. Cx(80,20)-202 Cy(80,20)- (b) When additional production is required, which model of stove results in the cost increasing at a higher rate? How can this be determined from the cost model? when additional production is required, the cost of the i -Select t stove is increasing at a higher rate because acay ? / x Submit Answer Save Progress

Explanation / Answer

C = 32 sqrt(xy) +185x +220y +1050

dC/dx = 32y/(2 sqrt xy) +185 , dC/dy = 32x/(2 sqrt xy) +220

dC/dx= 16y/(sqrt xy) +185 , dC/dy = 16x/(sqrt xy)+220

a. Cx(80,20) = 16(20)/sqrt(1600)) +185 = 193

Cy(80,20)=    16(80)/ 40 +220 = 252

b. When additional production is required, the cost of the y fireplace insert stoves is increasing at a higher rate because dC/dy > dC/dx

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