```{r data generation, echo = FALSE, results = "hide"} ## Base64-encoded PNG clipart images (CC0) ## created by base64enc::base64encode("file.png") banana <- 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" orange <- 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" pineapple <- 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" writeBin(base64enc::base64decode(banana), "banana.png") writeBin(base64enc::base64decode(orange), "orange.png") writeBin(base64enc::base64decode(pineapple), "pineapple.png") img0 <- sprintf("![%s](%s.png){width=\"0.85cm\"}", c("banana", "orange", "pineapple"), c("banana", "orange", "pineapple")) img <- function(x = "b") img0[factor(x, levels = c("b", "o", "p"))] ## prices ("in cent") b <- sample(20:99, size = 1) o <- sample(20:99, size = 1) p <- sample(199:499, size = 1) x <- c(b, o, p) ## three simple fruit baskets G <- sample(c("bbo", "bbp", "boo", "bpp", "oop", "opp"), 3) G <- t(sapply(G, function(x) sample(strsplit(x, "")[[1]]))) A <- t(apply(G, 1, function(x) table(factor(x, levels = c("b", "o", "p"))))) ## corresponding prices d <- A %*% x ## new fruit basket with all fruits and corresponding price sol <- sum(x) ``` Question ======== Given the following information: | | | | | | | | |:----------------:|:---:|:----------------:|:---:|:----------------:|:-:|-----------:| | `r img(G[1, 1])` | $+$ | `r img(G[1, 2])` | $+$ | `r img(G[1, 3])` | = | $`r d[1]`$ | | `r img(G[2, 1])` | $+$ | `r img(G[2, 2])` | $+$ | `r img(G[2, 3])` | = | $`r d[2]`$ | | `r img(G[3, 1])` | $+$ | `r img(G[3, 2])` | $+$ | `r img(G[3, 3])` | = | $`r d[3]`$ | Compute: | | | | | | | | |:------------:|:---:|:------------:|:---:|:------------:|:-:|-----------:| | `r img("b")` | $+$ | `r img("o")` | $+$ | `r img("p")` | = | $\text{?}$ | Solution ======== The information provided can be interpreted as the price for three fruit baskets with different combinations of the three fruits. This corresponds to a system of linear equations where the price of the three fruits is the vector of unknowns $x$: | | | | | | | |--------:|:-------------|--------:|:-------------|--------:|:-------------| | $x_1 =$ | `r img("b")` | $x_2 =$ | `r img("o")` | $x_3 =$ | `r img("p")` | The system of linear equations is then: $$ \begin{aligned} `r toLatex(A, escape = FALSE)` \cdot `r toLatex(matrix(paste0("x_", 1:3), ncol = 1), escape = FALSE)` & = & `r toLatex(matrix(d, ncol = 1), escape = FALSE)` \end{aligned} $$ This can be solved using any solution algorithm, e.g., elimination: $$ x_1 = `r b`, \, x_2 = `r o`, \, x_3 = `r p`. $$ Based on the three prices for the different fruits it is straightforward to compute the total price of the fourth fruit basket via: | | | | | | | | |:------------:|:---:|:------------:|:---:|:------------:|:-:|-----------:| | `r img("b")` | $+$ | `r img("o")` | $+$ | `r img("p")` | = | | | $x_1$ | $+$ | $x_2$ | $+$ | $x_3$ | = | | | $`r x[1]`$ | $+$ | $`r x[2]`$ | $+$ | $`r x[3]`$ | = | $`r sol`$ | Meta-information ================ exname: Fruit baskets (numeric) extype: num exsolution: `r fmt(sol)` extol: 0