Question

ikit 150 pasang. Seorang pemilik toko sepatu ingin mengisi tokonya dengan sepatu laki-laki paling sedikit 100 pasang dan sepatu wanita paling sedikit 150 pasang. Toko tersebut hanya dapat menampung 400 pasang sepatu. Keuntungan setiap pasang sepatu laki-laki adalah Rp 10.000,00 dan keuntungan setiap pasang sepatu wanita adalah Rp 5.000,00. Jika banyaknya sepatu laki-laki tidak boleh melebihi 150 pasang, maka tentukanlah keuntungan terbesar yang dapat diperoleh oleh pemilik toko.

Answer 1

Answer:

The biggest profit that can be obtained by the shop owner= IDR 2,750,000.

Step-by-step explanation:

We need to form a LPP( Linear Programming Problem) for the following problem and solve it to get the maximize the profit.

Let x denote the number of men's shoe and y denote the number of female shoes.

Maximize z= 10000x+5000y----------(1)

             x≥100 ( since a shoe store owner wants to fill his shop with at least    100 pairs of men's shoes )

            y≥150  (at least 150 pairs of women's shoes).

also x+y≤400   (The store can only accommodate 400 pairs of shoes).

         x≤150    (male shoes should not exceed 150 pairs).

⇒         100≤x≤150

Hence the optimal solution of an LPP always lie on the end points.

We have end points as:

(100,300), (150,250), (100,150),(150,150).

by putting these value in equation (1) we see which give the maximum solution.

for (100,300) i.e. x=100 and y=300:   z=2,500,000

for (150,250) i.e. x=150 and y=250:  z=2,750,000

for (100,150) i.e. x=100 and y=150: z=1,750,000

for (150,150) i.e. x=150 and y=150: z=2,250,000

Hence maximum profit is obtained at x=100 and y=300.

i.e. to maximize the profit:

Number of men's shoes to be kept in store=100

and number of women's shoes to be kept in store=300

The biggest profit that can be obtained by the shop owner= IDR 2,750,000.