Can you make detailed handwritten solution and GAMS programing solution

4.. - [28 points) Huntco produces tomato sauce at five different plants. The tomato sauce is stored at one of three warehouses (W/H). The per-ton cost (in hundreds of dollars) of producing tomato sauce at each plant and shipping it to each warehouse; capacity of the plants; and the fixed cost of setting up the plants are given in the below table. Cost to ($/ton) From plant W/H 1 W/H2 W/H 3 Capacity (tons) Fixed cost (>1,000 in $) Plant 1 8 10 12 300 35 Plant 2 7 5 7 200 Plant 3 6 5 300 Plant 4 5 6 7 200 42 Plant 5 7 6 5 400 40 Huntco has 4 customers. The cost of shipping a ton of sauce from each warehouse to each customer; customers' demand quantities; and the fixed cost of maintaining the warehouses are given below. 45 8 40 Page: 3 of 3 40 90 50 70 Cost to ($/ton) Fixed cost From W/H Customer 1 Customer 2 Customer 3 Customer 4 (x1,000 in $) W/H 1 80 30 W/H 2 70 60 80 40 W/H 3 80 30 50 60 30 Demand (tons) 200 300 150 250 We would like to meet the demand at minimum cost using an appropriate mathematical model. (a) [6 points] Decision variables? (b) [6 points] Objective and objective function? (c) (16 points] Constraints