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detailed solution 1. A businessman is currently overseeing the management of two local textile companies producing handwoven lfugao face masks: Company A and Company B.

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1. A businessman is currently overseeing the management of two local textile companies producing handwoven lfugao face masks: Company A and Company B. The prioe-demand equation and the cost function for the weekly production and sale of face masks in Company A are given. mpectively. by p = 60 2v\"? and are} = arm + a: where a: is the number of face masks that can be produced and sold weekly at a price of 11 pesos per piece. and CM] is the total cost (in pesos] of producing a: face masks per week. Similarly, the price-demand equation and the cost function for the weekly production and sale of face masks in Company B are given by p = 120 5V5 and (313:) = 1000 +1l'lm. Suppose both companies are currently producing 2: Answer the following questions. 250 face masks per week. [3} Find the marginal cost for each company at this production level. Interpret these [4] values. (b) Find the weekly total prot and marginal prot for each company at this pro- [IS] duction level. interpret these values. (c} Based on your answers in (a) and (b). would it be advisable for the businessman [2] to increase the production of face masks in Company A and/or in Company B? Justify your answer. 2. A rope is attached to a hook on the front of a boat and is passed through a pulley ['5] on a nearby deck. The pulley is h = 1.5 meters higher than the hook. If the rope is pulled into the dock at a rate of I15 meters per second. how fast is the boat approaching the dock when the boat is 2.0 meters away from the dock? Round your answer to four decimal places

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