The Cosmetic Co is a company that produces a variety of cosmetic creams and lotions. The creams and lotions are sold to various retailers at a price of $23.20 for each jar of face cream and $16.80 for each bottle of body lotion. Each of the products has a range of ingredients. with the key ones being silk powder, silk amino acids and aloe vera. Six months ago, silk worms were attacked by disease causing a huge reduction in the availability of silk powder and silk amino acids. The Cosmetic Co had to dramatically reduce production and make part of its workforce, which it had trained for over a number of years, redundant The company now wants to increase production again by ensuring that it uses the limited ingredients available to maximise profits by selling the optimum mix of creams and lotions. Due to the redundancies made earlier in the year, supply of skilled labour is now limited in the short-term to 160 hours (9,600 minutes) per week, although unskilled labour is unlimited The purchasing manager is confident that they can obtain 5,000 grams of silk powder and 1,600 grams of silk amino acids per week. All other ingredients are unlimited. The following information is available for the two products: Materials required Cream Lotion 2 grams Silk powder (S2.20 per gram) Silk amino acids (50 80 per gram) Aloe vera (1 40 per gram) 3 grams Igram 0.5 grams 4 grams 2 grams Labour required skilled (512 per hour) 4 minutes 5 minutes Labour required: unskilled (88 per hour) 3 minutes 15 minutes Each jar of cream sold generates a contribution of S9 per unit, whilst each bottle of lotion generates a contribution of S8 per unit. The maximum demand for lotions is 2,000 bottles per week, although demand for creams is unlimited. Fixed costs total up to $1,800 per week. The company does not keep inventory although if a product is partially complete at the end of one week, its production will be completed in the following week. Required: On the graph paper provided, usc linear programming to calculate the optimum number of each product that the Cosmetic Co. should make per week, assuming that it wishes to maximise contribution. Calculate the total contribution per week for the new production plan