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Model of Profit Maximization of the Giant Gourami (Osphronemus Goramy) Culture

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Model of Profit Maximization of the Giant Gourami (Osphronemus Goramy) Culture Omni-Akuatika, 13 (1): 54–59, 2017 ISSN: 1858-3873 print / 2476-9347 online Research Article Model of Profit Maximization of the Giant Gourami (Osphronemus goramy) Culture Dian Wijayanto1*), Faik Kurohman1, Ristiawan Agung Nugroho1 1Fakultas Perikanan dan Ilmu Kelautan Universitas Diponegoro *Corresponding author: [email protected] Received 7 November 2016; Accepted 16 April 2017; Available online 31 May 2017 ABSTRACT This research’ objective is to develop a model of profit maximization that can be applied to the giant gourami culture. The development of fish growth model uses polynomial growth function. Profit maximization process uses the first derivative of profit equation to culture time equal to zero. This research develop the equations to estimate the culture time to reach the size target of cultured fish. This research model can be applied in the giant gouramy culture. The giant gouramy culture can produce the maximum profit at 324 days with profit of IDR. 7.847.700 per culture cycle. To achieve size target of 500 g per fish, it needs 135 days of culture time. Keywords: bioeconomy, profit maximization, the giant gouramy 1. Introduction (1992), Springborn et al. (1992), Heap (1993), Strand and Mistiaen (1999), and Wijayanto The giant gouramy (Osphronemus (2014). Bjorndal (1988) estimated the optimal goramy) is one of major fisheries commodities harvest in fish culture used fish growth base on in Indonesia. It is also one of favorite food for Beverton-Holt model. Then, Arnason (1992), Indonesian cuisine. The giant gouramy culture Heap (1993), and Strand and Mistiaen (1999) has grown in Indonesia, including the Central also developed optimization profit model base Java province. The production progress of the on Beverton-Holt model. Springborn, et al giant gouramy has tendency to increase. In (1992) and Wijayanto (2014) developed the 2010, the production of the giant gouramy was profit maximization model in aquaculture base 56 889 tons and almost double in 2014 on von Bertalanffy fish growth model with (118.776 tons). Average of giant gouramy assumption of length exponent equal to 3 production is 20.5 percent during 2010 - 2015 (isometric). While this research used (KKP, 2015). polynomial fish growth. The purpose of this Production of giant gouramy is mainly research was to develop a model of profit from aquaculture in Indonesia. There are vary maximization fish culture that can be applied to methods of the giant gouramy culture in the giant gouramy culture base on polynomial Indonesia, both traditional or intensive growth model. methods. The giant gouramy farmers use methods of cultivation based on their habits, 2. Methodology knowledge and experiences, including the time of harvest. So, it is necessary to study the In this research, estimation to the giant optimization of profits in the giant gouramy gouramy growth function based on polynomial culture. This research focused on the giant growth model (second degree). Then, profit gouramy culture in monoculture and intensive maximization was developed base on the giant method. gouramy culture that developed in Central Java This research estimates the optimal profit province. This research used primary data and of the giant gouramy culture by using secondary data. This research used statistical bioeconomy approach. Fisheries bioeconomy is data and relevant references as secondary combination between fisheries and economic data, including biology of the giant gouramy. science. There were several researchers who Primary data was collected in three regencies, investigated the profit optimization of fish Magelang, Klaten and Wonosobo, which culture, including: Bjorndal (1988), Arnason Wijayanto et al., 2017, Model of Profit Maximization of the Giant Gourami 55 include prices and costs of the giant gouramy Wtb : fish weight (g) at tb. culture. Pi : fish prices (IDR per g) Ntb : fish populations (individual) at tb Fish growth model No : initial population of fish (individual) M : average mortality of fish per day In this research, we used the giant (individual per day) gouramy growth model follow this polynomial TC : total cost (IDR per cycle) at tb equation: Cp : accumulative procurement costs of artificial feed (IDR) at tb Wt= a t2 – b t (1) Cb : seed procurement costs (IDR per cycle) Ctk : accumative labor costs (IDR) at tb Where, Wt is the size of the fish (g) at the age Cd : accumative cost of equipment and of t days,’a’ is the intercept and ‘b’ is the slope. buildings depreciation (IDR) at tb Pp : feed prices (IDR per g) Costs, revenues and profits Qp : accumulated amount of feed utility (g) at tb In general, profit is revenue minus cost. Bo : early fish biomass (g) Revenue is affected by fish price and fish Wtbo: initial weight of fish seed (g per biomass. Fish biomass in aquaculture is individual) affected by individual fish growth and fish FCR : food conversion ratio mortality. While the component cost includes Ptk : labor costs per day (IDR per day) the cost of seed procurement, labor costs, feed Pd : depreciation rate of facilities and cost, cost of facilities and equipment. Artificial equipment (IDR per day) feed cost in aquaculture is affected by food conversion ratio (FCR), fish biomass progress Profit maximization and price of artificial feed. First derivative of profit (equation 2) to π = TR – TC culture time (tb) equal to zero could be use to (2) estimate the culture time to produce the TR = Btb.Pi maximal profit as the first order condition (3) (FOC). Second derivative of profit to culture Btb = Wtb.Ntb time equal to negative is the second order (4) condition (SOC). By using equation (1) to (13), Ntb = No-M.tb then we solved the profit become equation (14) (5) and (15): TR = Wtb.Pi.(No-M.tb) (6) π = Btb.Pi – Cp – Cb – Ctk – Cd TC = Cp+Cb+Ctk+Cd (14) (7) π = g.tb3 + h.tb2 + i.tb + j Cp = Pp.Qp (15) (8) Note: Qp = (Btb-Bo).FCR (9) g = a.(Pp.FCR.M - Pi.M) Bo = No.Wtbo h = Pi.a.No+Pi.b.M+2.Pp.FCR.a.tbo.M- (10) 2.Pi.a.tbo.M-Pp.FCR.a.No–Pp.FCR.b.M Ctk = Ptk.tb i = (11) 2.Pi.a.tbo.No+Pi.b.tbo.M+Pp.FCR.a.tbo2.M+Pp. Cd = Pd.tb FCR.b.No–Pi.a.tbo2.M–Pi.b.No- (12) 2.Pp.FCR.a.tbo.No-Pp.FCR.b.tbo.M–Pd– Ptk tb = t – tbo j = Pi.a.tbo2No - Pi.b.tbo.No - (13) Pp.FCR.a.tbo2.No + Pp.FCR.b.tbo.No + Note: Pp.FCR.Bo - Cb Π : profit (IDR per cycle) at time of culture (tb) = 0 = 3. g. tb + 2. h. tb + i (16) tb : time of culture (days) tbo : age of the fish seed at the beginning of Estimation of tb at equation (16) used quadratic cultivation (days) equation solution (Rosser, 2003). TR : total revenue (IDR per cycle) at tb Btb : biomass of fish at the time tb (g) 56 Omni-Akuatika Vol. 13 No. 1 May 2017 : 54 - 59 ()±().(). Equation (20) could be modified to tb = , .(.) equation (22) and then equation (22) could be (17) solved use the quadratic equation solution to ()().(). tb = estimate tbt. .(.) (18) 2 2 Wtt= a.tbo +2.a.tbo.tbt+a.tbt –b.tbo-b.tb ()().(). tb = (21) .(.) 2 2 0= a.tbt + (2.a.tbo-b).tbt + a.tbo –b.tbo- (19) Wtt (22) tb(,) = Target size of fish harvest (..)±(.) ..( .) . (23) Fish farmers can estimate the culture time base on fish size target use equation (20). 3. Result and Discussion This equation is modify of equation (1). 2 The giant gouramy growth Wtt= a (tbo+tbt) – b (tbo+tbt) (20) Using a previous study as a data (Rahmat, 2013), the growth rate of giant Note: gouramy was presented at Table 1 to develop the fish growth model. The result of polynomial Wtt : target of fish size (g) fish growth function follow the equation (24). tbt : culture time to produce Wtt Table 1. The giant gouramy growth Age (days) Individual Weight (g) 90 5 120 10 150 50 180 200 270 500 Source: Rahmat (2013) 600 500 500 400 300 200 2 200 Wt = 0,011.t - 1,0975.t R² = 0,9812 100 50 10 0 100 150 200 250 300 Age (days) Figure 1. The giant gouramy growth (g) Wijayanto et al., 2017, Model of Profit Maximization of the Giant Gourami 57 The result of polynomial fish growth cm (0.5 to 2.5 g). This stage need 2 function follow the equation (24). months. Stage 2: the giant gouramy culture to Wt = 0.011 t2 –1.0975 t (24) produce the seed with length of 5 to 8 cm (2.5 to 10.4 g). This stage need 2 R2 = 98% months. Stage 3: the giant gouramy culture to Subject to: produce the seed with length of 10 to Wt, t > 0 12 cm (20.4 to 35.2 g). This stage need 2 months. Wt ≤ Winf Stage 4: the giant gouramy culture to Rainboth (1996) and Froese, Thorson and produce the fish in consumption size Reyes Jr. (2013) estimated the value of W , with weight of 500 to 1 000 g. This inf stage need 4 months. Linf and length-weight equation of the giant gouramy, i.e. Winf = 6 512 g, Linf = 67.9 cm, and length-weight equation follow: W = In this research, we focused on the giant 0.01995 L3.01 gouramy culture to produce a fish to consumption. There were several assumption Profit maximization in this research. Base on research, culture time optimal At the present, there are variation of the to produce the maximal profit at 324 days. At giant gouramy culture methods. According to that time, the profit reach IDR 7 847 700 per Rahmat (2013), there were several stage of the cycle per pond.
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