Question

A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $15 per square meter. Material for the sides costs $9 per square meter. Find the cost of materials for the cheapest such container. (Round your answer to the nearest cent.)

Answer 1

Answer 2

hges 1. Let the base = x na meter width= ax metere (given) 1 height-y. . So volume = xx 2xxy - gety m ) ano azy = 10 Area of base = 2xxx = 222. cost of base = 2x2x15= 3ox? . Area of sides = 24 x xy + 2xaxxy - A4t*4: 578 cost of ride - 9x6xy = sy sky . Total cost a c(ay)= 30x²4 syzy. Constraint is p(x,y) = 2x²9-10 =0 Using Lagranges multipliere x, F(x,y) = [(x,y) +24(x,y) = 3om?+54 xy + 2(axy-lo). for getting the cheapest cost we have to equate Fx & fy equal to zero.

Гcot 514t 474 - о. Ғя - су + 22м2 о. — 0 узъ (*) ta7) = 0 . — 0) а) 1 = 0 , zht a1 -он) 2 - 34 x=0 is not possible. Now putting & value на о фон +ға Яt 4 xez) 4 -о. д ир» boxt ѕчя - Товч го соч - Sчт Putting this relation is pcery=o. а) эх = 10 з'я и к а) -- 1 ) = 2-с 2 че я: 10% : 2 - 412. ш. So a cheapest cost of material is е (а.са, д. 91а) - 30?1 счч - 2от 1 А пот“ Эtseчхар - 618. 19) +