Question

Create a line graph for an industry with economies of scale to show how much it costs to produce each given amount of a product. Suppose it costs $20,000 to set up and furnish a new restaurant. The cost for each meal the restaurant serves is$8. Use your math skills and the information above to answer the following questions: What is the cost per meal to produce ten meals? Fifty meals? One hundred meals? One thousand meals?

Solution

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Cost of setting up restaurant=$20000n=number of mealsCost for each n meals=$8nCost per meal to produce n meals=20000+(n8)nn=10Cost per meal to produce n meals=20000+(108)10=$2008n=50Cost per meal to produce n meals=20000+(508)50=$408n=100Cost per meal to produce n meals=20000+(1008)100=$208n=1000Cost per meal to produce n meals=20000+(10008)1000=$28\begin{align*} \text{Cost of setting up restaurant}&= \$20000 \\ \text{n=number of meals}\\ \text{Cost for each n meals}&=\$ 8*n \\ \text{Cost per meal to produce n meals}&= \frac{20000+(n*8)}{n}\\ \\ \\\text{n=10}\\ \text{Cost per meal to produce n meals}&= \frac{20000+(10*8)}{10}\\ &=\$2008 \\ \\ \\\\\text{n=50}\\ \text{Cost per meal to produce n meals}&= \frac{20000+(50*8)}{50}\\ \\ &=\$408 \\ \\ \\\\\text{n=100}\\ \text{Cost per meal to produce n meals}&= \frac{20000+(100*8)}{100}\\ \\ &=\$208\\ \\\\\text{n=1000}\\ \text{Cost per meal to produce n meals}&= \frac{20000+(1000*8)}{1000}\\ &=\$28\\ \end{align*}

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