Question

A small company can produce up to 200 handmade sandals a month. The monthly cost, C, of producing x sandals is C(x) = 1000 + 5x. . The monthly revenue, R, is given by R(x) = 75x - 0.4x2 . . Round your answer to the nearest integer.. At what production levels will the company lose money?. a. between 0 and 10 or between 150 and 190 pairs, inclusive . c. between 10 and 20 or between 50 and 100, inclusive . b. between 0 and 15 or between 160 and 200 pairs, inclusive . d. between 15 and 35 or between 75 and 125, inclusive .

Answer 1

I will assume the more likely selection of $10 per sandal as opposed to $0.05 per sandal. So with the formulas c = 1000 + 5x r = 75x - 0.4x^2 Sandals Cost Revenue Profit or Loss 0 $1,000.00 $0.00 -$1,000.00 1 $1,005.00 $74.60 -$930.40 2 $1,010.00 $148.40 -$861.60 3 $1,015.00 $221.40 -$793.60 4 $1,020.00 $293.60 -$726.40 5 $1,025.00 $365.00 -$660.00 6 $1,030.00 $435.60 -$594.40 7 $1,035.00 $505.40 -$529.60 8 $1,040.00 $574.40 -$465.60 9 $1,045.00 $642.60 -$402.40 10 $1,050.00 $710.00 -$340.00 11 $1,055.00 $776.60 -$278.40 12 $1,060.00 $842.40 -$217.60 13 $1,065.00 $907.40 -$157.60 14 $1,070.00 $971.60 -$98.40 15 $1,075.00 $1,035.00 -$40.00 16 $1,080.00 $1,097.60 $17.60 17 $1,085.00 $1,159.40 $74.40 18 $1,090.00 $1,220.40 $130.40 19 $1,095.00 $1,280.60 $185.60 20 $1,100.00 $1,340.00 $240.00 As you can see 16 sandals and up is profitable. At what production levels will the company lose money? a. between 0 and 10 or between 150 and 190 pairs, inclusive 150 and 190 c. between 10 and 20 or between 50 and 100, inclusive If you add up the profit between 10 and 20 you will get $-484 so 50 and 100 b. between 0 and 15 or between 160 and 200 pairs, inclusive 160 and 200 d. between 15 and 35 or between 75 and 125, inclusive Neither 15 and 35 or 75 and 125 will lose money.