The Problem An online clothing store is selling two products dresses and t-shirts. Each product is obtained from four suppliers: two dress suppliers (1 and 2) and two t-shirt suppliers (3 and 4). Each supplier offers a fixed price on their products for a corresponding minimum number of pieces to be purchased. However, the price depends on the size of the t-shirt or dress. Furthermore, the four suppliers offer policy in charging shipping fees. The problem is to determine how many of each product should be purchased from the four suppliers while minimizing the supply cost. The price (in $) per unit offered by the suppliers according to the size of the product to be purchased is presented in Table 1. Size Supplier Small Medium Large Extra Large Extar Extra Large 1 $4.40 $4.80 55.20 $5.60 2 $4.00 $4.40 $4.80 $5.20 3 $1.80 $2.00 52.20 $2.40 $2.60 4 Table-1 $2.20 $2.40 $2.60 $2.80 $3.00 Table 2 shows the information on the minimum number of pieces per purchase offered by the four suppliers. Supplier Minimum Number of units per order 1 2 3 4 10 6 30 25 Table-2 The demand for each product according to size is shown in Table-3. Product Dress T-shirt Small 40 40 Size Medium Large 20 30 50 60 Extra Large Extar Extra Large 10 0 30 20 Table-3 The shipping fees in (S) charged by the four suppliers based on the specified number of units per product are shown in Table-4.The owner wants to take the advantage of the free shipping offered by supplier 1 and 4. The owner also has a restriction on the shipping cost on supplier 2 and supplier 4 to be at most $ 20 for each supplier. Your job is to assist the store manager in determining the number of each product (the optimal product mix) to be purchased from the suppliers while minimizing the overall supply cost. You need to formulate and solve a linear program for this problem. Supplier 2 Supplier 3 Supplier 4 Units Shipping Cost Units Shipping Cost Units Shipping Cost Units Supplier 1 1 to 6 $3 1 to 10 $3.30 1 to 10 $302 10 or more Shipping Cost Free shipping 7 to 12 $4.80 11 to 20 $4.90 11 to 20 $4.80 13 to 18 $6.40 21 to 30 $6.60 21 to 30 $6.40 19 to 24 $8 31 to 40 $8.30 31 to 40 $8 26 to 30 $9.60 41 to 50 $9.90 41 or more Free Shipping 31 to 36 $11.20 51 to 60 $11.60 37 to 42 $12.80 61 to 70 $13.30 43 to 48 $14.40 71 to 80 $14.90 49 to 54 $16 81 to 901 $16.60 55 to 60 $17.60 91 to 100 $18.20 61 to 66 $19.20 101 to 110 $19.95 67 to 72 $20.80 111 to 120 $21.60 73 to 78 $22.40 121 to 130 $23.20 79 to 84 $24 131 to 140 $24.90 85 to 90 91 to 96 $25.60 141 to 150 $26.60 $27.20 151 to 160 $28.20 Table-4