ork County operates a yard waste recycling facility. The County collects four types of yard waste, (1) pre-treats the waste and then (2) processes the waste into saleable mulch products consisting of three different grades. The three grades with their respective mix specifications, processing costs and sale price are detailed below. Mulch Processing Cost Selling Price Grade Mix Specification per Pound per Pound Waste 1: Not more than 30% of the total A Waste 2: Not less than 50% of the total Waste 3: Not more that 40% of the total $4.00 $9.50 Waste 4: Exactly 20% of the total Waste 1: Not more that 50% of the total B Waste 2: Not less than 10% of the total 3.50 8.00 Waste 4: Exactly 20%% of the total C Waste 1: Not more that 60% of the total 3.00 6.50 The State requires the yard waste to receive a pre-treatment before processing. For this, the County is fully reimbursed in the form of a state grant. However, certain restrictions comply. The pounds per week available for each yard waste and the terms of the state grant are listed below. Yard Pounds/week Pre-Treatment Additional Restrictions Waste Available Cost per Pound (to meet the terms of the state grant) 1 3,000 $3.00 . For each type of yard waste, at least half of the pounds/week available should be collected and 2 2,500 6.00 pre-treated. 4,000 4.00 . Exactly $40,000 per week shall be spent A 1,000 5.00 to pre-treat the yard waste. a) Formulate this problem in linear programming terms by identifying all the activities, resources, benefits, and fixed requirements. (10 pts) b) Express this linear programming model in algebraic form to (1) determine the amount of each grade and (2) the mix of yard waste for each mulch grade, maximizing total weekly profit. (8 pts) c) Formulate and solve a spreadsheet model for this linear programming problem. Hint: Total Profit = $42,375 per week