SteelcoInc.manufactures I, W, U, H, and L beams. You are required to help Steelcodevelop an optimized work schedule for the 12 monthsof 2021. This year, under a similar demand and without any optimization tools, the company expects to clear around $60,000,000 in profits from these five products.To manufacture beams, Steelco purchases recycled steel for $400/ton and new steel for $600/ton.Due to the quality of the steel, only 80% of the recycled steel can be used to produce the products.Furthermore, at most 6,000 tonsof recycled steel can be purchased each month and only 5,000 tonsof new steel can be purchased at any month.Each ton of I, W, U, H, and L beams that is produced is sold by the price described in Table 1(see file Data Set -Steelco.xlsx in Canvas). Due to quality requirements, at least 40%, 20%, 60%, 10%, and 25% of I, W, U, H, and L beams, respectively, must be manufactured from new steel.Each ton of product heldover in inventory from one month to the next month costs the company $40/ton.If demand at each month is not met, then there is a penalty cost of $100/ton forI beams, $300/ton forW beams, $250/tons for U beams, $600/ton for H beams, and $1000/ton forLbeams.In such a case, the item is placed on backorder and the order must be shipped to the customer at some future time. Demand of each product over the next 12months is shown in Table 2(see file Data Set -Steelco.xlsx in Canvas).You must assume that you have nothing in inventory or items that are backordered, and that you must end 2021with the same condition

Table 2 - Demand of each Type of Beam over the Next 12 Months Month Beam

I W U H L

Jan 3500 2400 2700 2500 1200

Feb 1000 300 2400 1300 1500

Mar 700 900 3100 500 4300

Apr 1400 800 1600 3300 3900

May 2000 1400 3600 2100 800

Jun 2000 900 3700 1500 200

Jul 1000 900 2000 1000 3500

Aug 1700 1000 3100 800 1200

Sep 2000 1700 3300 4100 2200

Oct 3000 1500 3000 2000 1300

Nov 1000 1900 2000 2800 4100

Dec 700 2000 3100 100 1000

Table 1 - Selling Price of Each Type of Beam

Beam Selling Price ($/ton)

I $1,000

W $750

U $1,500

H $1,200

L $800

could you help with setting up the linear program ?