The Sweet Candy Company includes in its product line a number of different mixed nut products. The Chalet nut mix is required to have no more than 25 percent peanuts and no less than 40 percent almonds. The nuts available, their prices and their availabilities this month are as follows:price availabilitypeanuts 20cents/lb 400lbswalnuts 35cents/lb NO limitalmonds 50cents/lb 200lbsThe Chalet mix sells for 90 cents per lb. At most 700 lbs can be mixed per month in questions (a), (b) below. (a) Formulate and solve the appropriate model for this problem. (b) The company would like to incorporate into the analysis its second major mixed nut line, the Hovel line. The Hovel mix can contain no more than 60 percent peanuts and no less than 20 percent almonds. Hovel sells for 50 cents per lb. Modify your model appropriately and solve. What is the scarcest resource? By how much the profit contribution will increase if one more pound of (i) peanuts was available. Similarly find if one more pound of (ii) almonds or (iii) walnuts was available. (c) Note in (b) that Hovel did not come into the optimal solution. What increase in the price of Hovel will make it profitable? Hint: use sensitivity analysis ‐ objective row ranges. Hints for Product Mix problem: The decision variables are of course the amounts of nuts to mix (lbs). In part (b) you will need twice as many variables; also note that the two products now share all original resources (materials and process capacity). In part (c) the "objective coefficient ranges" are needed. In LINGO, after you solve the problem, choose from the LINGO drop‐down menu "Range". This will copy the ranges in your output report. If LINGO responds with "ranges are not enabled" go to LINGO‐Options and select from the menu "Dual Computations" the item "Prices and Ranges"; you need to solve again. You should find the following as the range for the price of Hovel mix to stay optimal: .05375 as allowable increase and infinity as is the allowable decrease. In any case, use this range numbers in answering Question (c)