$[$QX$]$: $6-38$ North Manufacturing has a demand for $1,000$ pumps each year. The cost of a pump is$$50.$ It costs North Manufacturing $$40$ to place an order, and the carrying cost is $25\%$ of the unit cost.If pumps are ordered in quantities of $200,$ North Manufacturing can get a $3\%$ discount on the cost of the pumps. Should North Manufacturing order $200$ pumps at a time and take the $3\%$ discount?