A dietician is asked to design a special diet supplement using two foods. Each ounce of food Each ounce of food X contains 30 units of calcium and each ounce of food Y contains 20 units of calcium. The minimum daily requirement in the diet is 80 units of calcium. Sketch a graph of the solution of the linear inequality that represents the different numbers of units of food X and food Y required.

Question

Quizplus · Accepted Answer

Let x represent the number of ounces of food X and y represent the number of ounces of food Y required to meet the minimum daily requirement of 80 units of calcium.
The total units of calcium can be expressed as 30x + 20y, and we want this to be greater than or equal to 80.
Thus, the inequality is 30x + 20y ≥ 80.
To graph this inequality, we can first graph the line 30x + 20y = 80 by finding the x- and y-intercepts. 
x-intercept: 30x + 20y = 80 → 30x = 80 → x = 8/3 
y-intercept: 30x + 20y = 80 → 20y = 80 → y = 4 
Plot the x- and y-intercepts and draw a line passing through them to get the line 30x + 20y = 80.
To determine which side of the line to shade, we can test a point not on the line, such as (0,0).
30(0) + 20(0) ≥ 80 is false, so we shade the side not containing the origin. 
The resulting graph is in choice B.

A Dietician Is Asked to Design a Special Diet Supplement