Theory (40 points) 1. The cost per day of running a hospital is 200,000 +0.002x2 dollars, where x = patients served per day. What size hospital minimizes the per-patient cost of running the hospital?...

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Theory (40 points) 1. The cost per day of running a hospital is 200,000 +0.002x2 dollars, where x = patients served per day. What size hospital minimizes the per-patient cost of running the hospital? Show your work and you cannot use the python code. (20 points) Refer to example on page 9. 2. If a company spends $a on advertising and charges a price of $p per unit, then it sells 1,000 – 100p +20a1/2 units of the product. The per-unit cost of producing the product is $6. (1) What is the objective function to maximize profit? And (2) what is the lower bounds for a and p? Show your work (20 points). Practice (60 points) 1. Using “optimize.mimize” in scipy, solve the linear problem (use method “SLSQP”). Please refer to this code. (30 points) max x3 + x4 a. x1 + x2 + x3 + x4 = 700 b. x3 - 0.5x4 =0 c. x1 + x2 <= 450="" d.="" x2="" +="" x3=""><= 300="" e.="" x2="" +="" x3=""><= x1="" +="" x4="" f.="" x1="">=0, x2>=0, x3>=0, x4>=0 2. The objective function, . We want to find the optimal pair (x,y) to minimize this function with (). (30 points) a. Construct 2-dimensional uniform grid with dx=0.1 and dy=0.1. x=-2:0.1:2 and y =-2:0.1:2. b. Calculate the function value at the grid and find the minimum and the corresponding pair (x*,y*). c. Construct a refined uniform grid near the optimal pair (x*,y*) in part b like with dx=0.01 and dy = 0.01. d. Calculate the function value at the grid and find the minimum and the corresponding pair (x**,y**).
Answered Same DayNov 01, 2021

Answer To: Theory (40 points) 1. The cost per day of running a hospital is 200,000 +0.002x2 dollars, where x =...

Sampad Swarup answered on Nov 04 2021
148 Votes
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"cost_per_day = 200000 + 0.002*x*x\n",
"x = number_of_patient\n",
"let y is a function that calculate cost per capita\n",
"then \n",
"y = cost_per_day /x \n",
"to find min or max y we have to find the equetion of the slope of the function and equate it to zero so we can find the min and max values.\n",
"So \n",
"dy/dx = 0\n",
"=> -200,000/x**2 + 0.002 = 0\n",
"=> x = 10,000\n",
"\n",
"To check whether the value is a minima or maxima we have to take the derivative of the slope and put the value we got from our first derivative.\n",
"\n",
"z = d/dx(dx/dy)\n",
"=> z = d/dx(-200,000/x**2)\n",
"=> z = 400,000/x**3 \n",
"\n",
"then at 10,000 the z is positive so it is the minima of the function \n",
"\n",
"Hance for 10,000 patient the cost per capita will be minimum."
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"a = price_of_adv\n",
"p = price_per_unit\n",
"\n",
"total_unit_sell = 1000 - 100p + 20*a**1/2\n",
"manufacture_cost_per_unit = 6$\n",
"profit_per_unit = p-6\n",
"\n",
"total_profit = total_unit_sell * profit_per_unit\n",
"total_profit_fun = (1000 - 100p +...
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