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4. Each week, a manufacturer of candles is able to produce f(H, M) candles if their employees work a total of H hours and they use their candle production machines for a total of M hours. Each employee earns a wage of $20 per hour and due to electricity and maintenance, the machines cost about $50 per hour to run. They aim to maximize their production, given their budget of $8000 per week. (a) (3 points) A contour map for the production function f(HM) is shown below. Please use this map to determine how the candle manufacturer should operate in order to maximize their pro- duction, subject to their budget constraint. Sketch on the graph as needed, then complete the sentences on the right. M (hours 200 100 -35000 30000 25000 20000 15000 If the candle manufacturer is currently operating with a budget of $8000 per week, they should use employee hours, and machine hours. 500 300 200 H hours) (b) (2 points) According to the method of Lagrange multipliers, the manufacturer is currently op- erating to maximize production, given their budget of $8000 per week. In plain language, what is the meaning of X = 2.5? Please fill in the appropriate bubble with a dark colour. If their budget were to increase by $2, they could produce about 5 more candles. If their budget were to increase by $5, they could produce about 2 more candles. If they use 2 more worker hours, they could produce about 5 more candles. If they use 5 more machine hours, they could produce about 2 more candles. Other: (e) (3 points) In order to double check that they are indeed maximizing production, the company uses the second derivative test. At the point (H. M) found in (a), they find that D- ff- am)